1rBTX 06. ESTADÍSTICA/1.6.1 Gràfics 1.6.1.11 Diagrama de barres:interpretar Observa el gràfic següent sobre transport (en milers de passatgers)  i contesta a les preguntes:
#G

El bus correspon a la 1a columna, el cotxe a la segona, el metro a la tercera, i el tren a la quarta.
És un diagrama del tipus {#1}.
Segons aquest diagrama, el mitjà de transport més utilitzat és el {#2}.
Quanta gent utilitza transport en total? {#3}

]]> El total de transportats es calcula sumant #n_1 + #n_2 + #n_3 + #n_4

]]> 3.0000000 0.5000000 0 <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>màxim</mi><mo>(</mo><mi>n_1</mi><mo>,</mo><mi>n_2</mi><mo>,</mo><mi>n_3</mi><mo>,</mo><mi>n_4</mi><mo>)</mo><mo>=</mo><mi>n_3</mi></mrow><mtable><mtr><mtd><mi>t_1</mi><mo>=</mo><mi>Bus</mi></mtd></mtr><mtr><mtd><mi>t_2</mi><mo>=</mo><mi>Cotxe</mi></mtd></mtr><mtr><mtd><mi>t_3</mi><mo>=</mo><mi>Tren</mi></mtd></mtr><mtr><mtd><mi>t_4</mi><mo>=</mo><mi>Metro</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>t_1</mi><mo>=</mo><mi>Cotxe</mi></mtd></mtr><mtr><mtd><mi>t_2</mi><mo>=</mo><mi>Metro</mi></mtd></mtr><mtr><mtd><mi>t_3</mi><mo>=</mo><mi>Bus</mi></mtd></mtr><mtr><mtd><mi>t_4</mi><mo>=</mo><mi>Tren</mi></mtd></mtr></mtable></apply></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mfenced><mrow><mi>n_1</mi><mo>+</mo><mi>n_2</mi><mo>+</mo><mi>n_3</mi><mo>+</mo><mi>n_4</mi></mrow></mfenced><mo>*</mo><mn>1000</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>200</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>400</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Cotxe</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000000</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 1.6.1.21 Diagrama de sectors:interpretar Observa el gràfic següent corresponent al nombre de fills per família en una població i contesta a les preguntes:
#G


És un diagrama del tipus {#1}.
Segons aquest diagrama, la majoria de famílies tenen {#2} fills/es.
Quina és la opció minoritària? Tenir {#3} fills.
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xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>800</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>700</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>650</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 1.6.1.31Q Diagrama de barres: associar Quin és el gràfic que correspon a la taula de freqüències següent?

xi ni
taronja #n_1
verd #n_2
cian #n_3
groc #n_4


a) #G
b) #H

És el gràfic {#1}

]]> 1.0000000 0.5000000 0 <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>Groc</mi><mo>→</mo><mi>n_1</mi><mo>,</mo><mi>Cian</mi><mo>→</mo><mi>n_2</mi><mo>,</mo><mi>Verd</mi><mo>→</mo><mi>n_3</mi><mo>,</mo><mi>Taronja</mi><mo>→</mo><mi>n_4</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_finestra</mi><mo>=</mo><mn>600</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>600</mn><mo>,</mo><mi>centre</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mn>9</mn><mo>,</mo><mn>240</mn><mo>)</mo><mo>,</mo><mi>altura</mi><mo>=</mo><mn>550</mn><mo>,</mo><mi>mostrar_eixos</mi><mo>=</mo><mi>fals</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math 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open="["><mrow><mi>Taronja</mi><mo>→</mo><mi>n_1</mi><mo>,</mo><mi>Verd</mi><mo>→</mo><mi>n_2</mi><mo>,</mo><mi>Cian</mi><mo>→</mo><mi>n_3</mi><mo>,</mo><mi>Groc</mi><mo>→</mo><mi>n_4</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T2</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_finestra</mi><mo>=</mo><mn>600</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>600</mn><mo>,</mo><mi>centre</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mn>9</mn><mo>,</mo><mn>240</mn><mo>)</mo><mo>,</mo><mi>altura</mi><mo>=</mo><mn>550</mn><mo>,</mo><mi>mostrar_eixos</mi><mo>=</mo><mi>fals</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>=</mo><mi>diagrama</mi><mo>(</mo><mi>T2</mi><mo>,</mo><mi>M</mi><mo>,</mo><mfenced close="}" open="{"><mtable 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>250</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 1.6.1.41 Diagrama Percentatge Interpretar En una població imaginària, la taxa d'atur presenta l'evolució següent:

#G




En quin any es va produir una disminució de l'atur? l'any {#1}
En quin tant per cent va disminuir l'atur? {#2} El 2008 l'atur era del #n_1 %
Si la població tenia #h habitants l'1 de gener de 2008,i augmenta d'un #a % anual (atenció, és com un interès compost), quants aturats hi ha al final del 2012? {#3}

]]> 3.0000000 0.5000000 0 <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="]" open="["><mrow><mo>&quot;</mo><mn>2008</mn><mo>&quot;</mo><mo>→</mo><mi>n_1</mi><mo>,</mo><mo>&quot;</mo><mn>2009</mn><mo>&quot;</mo><mo>→</mo><mi>n_2</mi><mo>,</mo><mo>&quot;</mo><mn>2010</mn><mo>&quot;</mo><mo>→</mo><mi>n_3</mi><mo>,</mo><mo>&quot;</mo><mn>2011</mn><mo>&quot;</mo><mo>→</mo><mi>n_4</mi><mo>,</mo><mo>&quot;</mo><mn>2012</mn><mo>&quot;</mo><mo>→</mo><mi>n_5</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mfenced close="}" open="{"><mtable 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xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2010</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 1rBTX 06. ESTADÍSTICA/1.6.2 Unidimensional 1.6.2.10DT  

Mitjana
Si tenim poques dades, el més fàcil és sumar els diferents valors de la variable xi i dividir aquesta suma pel nombre d'elements de la població.

Si el nombre de dades és més elevat, la mitjana es calcula amb l'expressió:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»§#175;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«munderover mathcolor=¨#003300¨»«mo mathvariant=¨bold¨»§#8721;«/mo»«mrow»«mi mathvariant=¨bold¨»i«/mi»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mi mathvariant=¨bold¨»j«/mi»«/munderover»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»x«/mi»«mi mathvariant=¨bold¨»i«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»f«/mi»«mi mathvariant=¨bold¨»i«/mi»«/msub»«/math»
Si xi són els valors que pren la variable, fi la freqüència relativa de cada un d'aquests valors i j el nombre de valors que pren la variable. El més pràctic és emprar una taula de freqüències:
xi ni fi xi·fi
3 12 0,6 1,8
4 6 0,3 1,2
5 2 0,1 0,5
Total 20 1 3,5
i completar-la fins a trobar la mitjana, 3,5.
]]> 0.0000000 0.0000000 0 1.6.2.11Q Mitjana10Notes  Determina, amb la calculadora, la mitjana de les notes següents:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»7«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»10«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«/mstyle»«/math»


Resposta arrodonida als dècims.

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_2</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_3</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_4</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_5</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_6</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_7</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_8</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_9</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_10</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mfrac><mrow><mi>n_1</mi><mo>+</mo><mi>n_2</mi><mo>+</mo><mi>n_3</mi><mo>+</mo><mi>n_4</mi><mo>+</mo><mi>n_5</mi><mo>+</mo><mi>n_6</mi><mo>+</mo><mi>n_7</mi><mo>+</mo><mi>n_8</mi><mo>+</mo><mi>n_9</mi><mo>+</mo><mi>n_10</mi></mrow><mn>10</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>10</mn><mo>*</mo><mi>r_1</mi><mo>)</mo></mrow><mn>10</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerància</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Suma les 10 dades i divideix per 10.

]]> 1.6.2.12Q Mitjana10Temperatures  Determina, amb la calculadora, la mitjana de les temperatures següents:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»7«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»10«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«/mstyle»«/math»


Resposta arrodonida als dècims.

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_7</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_8</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_9</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_10</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mfrac><mrow><mi>n_1</mi><mo>+</mo><mi>n_2</mi><mo>+</mo><mi>n_3</mi><mo>+</mo><mi>n_4</mi><mo>+</mo><mi>n_5</mi><mo>+</mo><mi>n_6</mi><mo>+</mo><mi>n_7</mi><mo>+</mo><mi>n_8</mi><mo>+</mo><mi>n_9</mi><mo>+</mo><mi>n_10</mi></mrow><mn>10</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>10</mn><mo>*</mo><mi>r_1</mi><mo>)</mo></mrow><mn>10</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerància</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Suma les 10 dades i divideix per 10.

]]> 1.6.2.13Q IncrementMitjana10Temperatures  Les temperatures de la primera quinzena de febrer del 2015, en un observatori, han estat les següents:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»7«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»10«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»n«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»11«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»n«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»12«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»n«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»13«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»n«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»14«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»n«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»15«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«/mstyle»«/math»

Durant els mateixos dies de febrer del 2016, la temperatura ha estat cada dia #w1º superior a la del 2015.

Quina ha estat la mitjana d'aquests 15 dies l'any 2016?


Resposta arrodonida als dècims.

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_7</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_8</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_9</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_10</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_13</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_14</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_15</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>15</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mfrac><mrow><mi>n_1</mi><mo>+</mo><mi>n_2</mi><mo>+</mo><mi>n_3</mi><mo>+</mo><mi>n_4</mi><mo>+</mo><mi>n_5</mi><mo>+</mo><mi>n_6</mi><mo>+</mo><mi>n_7</mi><mo>+</mo><mi>n_8</mi><mo>+</mo><mi>n_9</mi><mo>+</mo><mi>n_10</mi><mo>+</mo><mi>n_11</mi><mo>+</mo><mi>n_12</mi><mo>+</mo><mi>n_13</mi><mo>+</mo><mi>n_14</mi><mo>+</mo><mi>n_15</mi></mrow><mn>15</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>10</mn><mo>*</mo><mi>r_1</mi><mo>)</mo></mrow><mn>10</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>r2</mi><mo>+</mo><mi>w1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sum</mi><mo>=</mo><mi>n_1</mi><mo>+</mo><mi>n_2</mi><mo>+</mo><mi>n_3</mi><mo>+</mo><mi>n_4</mi><mo>+</mo><mi>n_5</mi><mo>+</mo><mi>n_6</mi><mo>+</mo><mi>n_7</mi><mo>+</mo><mi>n_8</mi><mo>+</mo><mi>n_9</mi><mo>+</mo><mi>n_10</mi><mo>+</mo><mi>n_11</mi><mo>+</mo><mi>n_12</mi><mo>+</mo><mi>n_13</mi><mo>+</mo><mi>n_14</mi><mo>+</mo><mi>n_15</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerància</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>,</mo><mi>w1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8.9</mn><mo>,</mo><mn>1.9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sum</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>133</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10.8</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Calcula la mitjana com sempre i com que l'augment de #w1º ha estat el mateix cada dia, la mitjana ha pujat de #w1º

]]> 1.6.2.15Q MitjanaPonderada10Notes  Les notes d'un estudiant han estat les següents:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»7«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»10«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«/mstyle»«/math»

Si les 6 primeres representen un 40% de la nota i les 4 últimes un 60%, quina qualificació obtindrà aquest estudiant?

 

Resposta arrodonida als dècims.

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_2</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_3</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_4</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_5</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_6</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_7</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_8</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_9</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_10</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>4</mn><mo>*</mo><mfenced><mfrac><mrow><mi>n_1</mi><mo>+</mo><mi>n_2</mi><mo>+</mo><mi>n_3</mi><mo>+</mo><mi>n_4</mi><mo>+</mo><mi>n_5</mi><mo>+</mo><mi>n_6</mi></mrow><mn>6</mn></mfrac></mfenced><mo>+</mo><mn>0</mn><mo>.</mo><mn>6</mn><mo>*</mo><mfenced><mfrac><mrow><mi>n_7</mi><mo>+</mo><mi>n_8</mi><mo>+</mo><mi>n_9</mi><mo>+</mo><mi>n_10</mi></mrow><mn>4</mn></mfrac></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mfrac><mfenced><mrow><mi>n_1</mi><mo>+</mo><mi>n_2</mi><mo>+</mo><mi>n_3</mi><mo>+</mo><mi>n_4</mi><mo>+</mo><mi>n_5</mi><mo>+</mo><mi>n_6</mi></mrow></mfenced><mn>6</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>=</mo><mfrac><mfenced><mrow><mi>n_7</mi><mo>+</mo><mi>n_8</mi><mo>+</mo><mi>n_9</mi><mo>+</mo><mi>n_10</mi></mrow></mfenced><mn>4</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>10</mn><mo>*</mo><mi>r_1</mi><mo>)</mo></mrow><mn>10</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerància</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi><mo>,</mo><mi>n_2</mi><mo>,</mo><mi>n_3</mi><mo>,</mo><mo> </mo><mi>n_4</mi><mo>,</mo><mi>n_5</mi><mo>,</mo><mi>n_6</mi><mo>,</mo><mi>m1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7.8</mn><mo>,</mo><mn>9.9</mn><mo>,</mo><mn>7.1</mn><mo>,</mo><mn>4.6</mn><mo>,</mo><mn>2.1</mn><mo>,</mo><mn>9.6</mn><mo>,</mo><mn>6.85</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_7</mi><mo>,</mo><mi>n_8</mi><mo>,</mo><mi>n_9</mi><mo>,</mo><mi>n_10</mi><mo>,</mo><mi>m2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.9</mn><mo>,</mo><mn>3.1</mn><mo>,</mo><mn>8.7</mn><mo>,</mo><mn>4.2</mn><mo>,</mo><mn>4.475</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5.4</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Calcula la mitjana de les 6 primeres notes, #m1, que representen el 40% de la nota;
calcula la mitjana de les 4 últimes notes, #m2, que representen el 60%.

]]> 1.6.2.16Q MitjanaPonderadaClasse  Si en una classe hi ha #f noies que han tret un #n1 i #m noies que han tret un #n2,

quina és la mitjana de la classe?



Resposta arrodonida als dècims.

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>m</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mfenced close="|" open="|"><mrow><mi>n1</mi><mo>-</mo><mi>n2</mi></mrow></mfenced><mo>⩾</mo><mn>2</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>f</mi><mo>+</mo><mi>m</mi><mo>=</mo><mn>30</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>f</mi><mo>≠</mo><mi>m</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mfrac><mrow><mi>f</mi><mo>*</mo><mi>n1</mi><mo>+</mo><mi>m</mi><mo>*</mo><mi>n2</mi></mrow><mn>30</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>10</mn><mo>*</mo><mi>r_1</mi><mo>)</mo></mrow><mn>10</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerància</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>,</mo><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>,</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>,</mo><mi>n2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn><mo>,</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4.9</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Pondera la mitjana amb el nombre de nois i de noies

]]> 1.6.2.17Q TrobarNotaPonderadaAprovar  A la selectivitat, la nota de l'expedient compta per un 60% de la nota i la nota de les proves generals per un 40%.

Si la teva nota d'expedient és de #n1, quina nota has de treure a les proves de selectivitat per tenir una mitjana de #n2 ?

 



Resposta arrodonida als dècims.

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n1</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>70</mn><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>6</mn></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>4</mn></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>100</mn><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>R</mi><mo>=</mo><mi>resol</mi><mfenced><mrow><mn>0</mn><mo>.</mo><mn>6</mn><mo>*</mo><mi>n1</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>=</mo><mi>n2</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>10</mn><mo>*</mo><msub><mi>R</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>)</mo></mrow><mn>10</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>n2</mi><mo>-</mo><mi>n1</mi><mo>&gt;</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>sol</mi><mo>&lt;</mo><mn>10</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerància</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>,</mo><mi>n2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5.4</mn><mo>,</mo><mn>6.3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mn>7.65</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7.7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Si x és la nota que has de treure, pots calcular x resolent l'equació:

0,6 · #n1 + 0.4 · x = #n2

]]> 1.6.2.18Q MitjanaDeTaula Determina la mitjana d'aquesta distribució (als centèsims)

Xi Fi
#x1 #n_1
#x2 #n_2
#x3 #n_3
#x4 #n_4
#x5 #n_5
#x6 #n_6
]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>11</mn><mo>,</mo><mn>21</mn><mo>,</mo><mn>31</mn><mo>,</mo><mn>41</mn><mo>,</mo><mn>51</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x4</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x5</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x6</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mi>n_1</mi><mo>+</mo><mi>n_2</mi><mo>+</mo><mi>n_3</mi><mo>+</mo><mi>n_4</mi><mo>+</mo><mi>n_5</mi><mo>+</mo><mi>n_6</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mo>(</mo><mi>s</mi><mo> </mo><mi>mod</mi><mo> </mo><mn>10</mn><mo>)</mo><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mfrac><mi>n_1</mi><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mfrac><mi>n_2</mi><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi><mo>=</mo><mfrac><mi>n_3</mi><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f4</mi><mo>=</mo><mfrac><mi>n_4</mi><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f5</mi><mo>=</mo><mfrac><mi>n_5</mi><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f6</mi><mo>=</mo><mfrac><mi>n_6</mi><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>x1</mi><mo>*</mo><mi>f1</mi><mo>+</mo><mi>x2</mi><mo>*</mo><mi>f2</mi><mo>+</mo><mi>x3</mi><mo>*</mo><mi>f3</mi><mo>+</mo><mi>x4</mi><mo>*</mo><mi>f4</mi><mo>+</mo><mi>x5</mi><mo>*</mo><mi>f5</mi><mo>+</mo><mi>x6</mi><mo>*</mo><mi>f6</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>m1</mi><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerància</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mi>x3</mi><mo>,</mo><mi>x4</mi><mo>,</mo><mi>x5</mi><mo>,</mo><mi>x6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>51</mn><mo>,</mo><mn>52</mn><mo>,</mo><mn>53</mn><mo>,</mo><mn>54</mn><mo>,</mo><mn>55</mn><mo>,</mo><mn>56</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi><mo>,</mo><mi>n_2</mi><mo>,</mo><mi>n_3</mi><mo>,</mo><mi>n_4</mi><mo>,</mo><mi>n_5</mi><mo>,</mo><mi>n_6</mi><mo>,</mo><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn><mo>,</mo><mn>18</mn><mo>,</mo><mn>12</mn><mo>,</mo><mn>15</mn><mo>,</mo><mn>17</mn><mo>,</mo><mn>11</mn><mo>,</mo><mn>90</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>,</mo><mi>f2</mi><mo>,</mo><mi>f3</mi><mo>,</mo><mi>f4</mi><mo>,</mo><mi>f5</mi><mo>,</mo><mi>f6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>17</mn><mn>90</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>,</mo><mfrac><mn>2</mn><mn>15</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>6</mn></mfrac><mo>,</mo><mfrac><mn>17</mn><mn>90</mn></mfrac><mo>,</mo><mfrac><mn>11</mn><mn>90</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>160</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>53.33</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">8</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ho pots fer amb un Excel.

]]> 1.6.2.18Q MitjanaDeTaula_2 Determina la mitjana d'aquesta distribució (als centèsims)

Xi Fi
#x1 #n_1
#x2 #n_2
#x3 #n_3
#x4 #n_4
#x5 #n_5
#x6 #n_6
]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>100</mn><mo>,</mo><mn>200</mn><mo>,</mo><mn>300</mn><mo>,</mo><mn>400</mn><mo>,</mo><mn>500</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mn>10</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mn>20</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x4</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mn>30</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x5</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mn>40</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x6</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mn>50</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mi>n_1</mi><mo>+</mo><mi>n_2</mi><mo>+</mo><mi>n_3</mi><mo>+</mo><mi>n_4</mi><mo>+</mo><mi>n_5</mi><mo>+</mo><mi>n_6</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mo>(</mo><mi>s</mi><mo> </mo><mi>mod</mi><mo> </mo><mn>10</mn><mo>)</mo><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mfrac><mi>n_1</mi><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mfrac><mi>n_2</mi><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f3</mi><mo>=</mo><mfrac><mi>n_3</mi><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f4</mi><mo>=</mo><mfrac><mi>n_4</mi><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f5</mi><mo>=</mo><mfrac><mi>n_5</mi><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f6</mi><mo>=</mo><mfrac><mi>n_6</mi><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>x1</mi><mo>*</mo><mi>f1</mi><mo>+</mo><mi>x2</mi><mo>*</mo><mi>f2</mi><mo>+</mo><mi>x3</mi><mo>*</mo><mi>f3</mi><mo>+</mo><mi>x4</mi><mo>*</mo><mi>f4</mi><mo>+</mo><mi>x5</mi><mo>*</mo><mi>f5</mi><mo>+</mo><mi>x6</mi><mo>*</mo><mi>f6</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>m1</mi><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerància</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mi>x3</mi><mo>,</mo><mi>x4</mi><mo>,</mo><mi>x5</mi><mo>,</mo><mi>x6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn><mo>,</mo><mn>310</mn><mo>,</mo><mn>320</mn><mo>,</mo><mn>330</mn><mo>,</mo><mn>340</mn><mo>,</mo><mn>350</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi><mo>,</mo><mi>n_2</mi><mo>,</mo><mi>n_3</mi><mo>,</mo><mi>n_4</mi><mo>,</mo><mi>n_5</mi><mo>,</mo><mi>n_6</mi><mo>,</mo><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>,</mo><mn>19</mn><mo>,</mo><mn>17</mn><mo>,</mo><mn>16</mn><mo>,</mo><mn>12</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>80</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>,</mo><mi>f2</mi><mo>,</mo><mi>f3</mi><mo>,</mo><mi>f4</mi><mo>,</mo><mi>f5</mi><mo>,</mo><mi>f6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>9</mn><mn>80</mn></mfrac><mo>,</mo><mfrac><mn>19</mn><mn>80</mn></mfrac><mo>,</mo><mfrac><mn>17</mn><mn>80</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>,</mo><mfrac><mn>3</mn><mn>20</mn></mfrac><mo>,</mo><mfrac><mn>7</mn><mn>80</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>323</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>323.</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">8</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ho pots fer amb un Excel.

]]> 1.6.2.20DT Moda  

Moda
És el valor de la variable xi que té la freqüència més alta.
]]> 0.0000000 0.0000000 0 1.6.2.21Q Moda10valors  Determina la moda de les notes següents:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»7«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»10«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«/mstyle»«/math»


Format: 5 (si no és única escriu les modes {22,24})

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_7</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_8</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_9</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_10</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>n_1</mi><mo>=</mo><mi>n_7</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>n_4</mi><mo>=</mo><mi>n_6</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>compta_element</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>n_1</mi><mo>,</mo><mi>n_2</mi><mo>,</mo><mi>n_3</mi><mo>,</mo><mi>n_4</mi><mo>,</mo><mi>n_5</mi><mo>,</mo><mi>n_6</mi><mo>,</mo><mi>n_7</mi><mo>,</mo><mi>n_8</mi><mo>,</mo><mi>n_9</mi><mo>,</mo><mi>n_10</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>n_1</mi><mo>,</mo><mi>n_2</mi><mo>,</mo><mi>n_3</mi><mo>,</mo><mi>n_4</mi><mo>,</mo><mi>n_5</mi><mo>,</mo><mi>n_6</mi><mo>,</mo><mi>n_7</mi><mo>,</mo><mi>n_8</mi><mo>,</mo><mi>n_9</mi><mo>,</mo><mi>n_10</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>moda</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi><mo>,</mo><mi>n_2</mi><mo>,</mo><mi>n_3</mi><mo>,</mo><mi>n_4</mi><mo>,</mo><mi>n_5</mi><mo>,</mo><mi>n_6</mi><mo>,</mo><mi>n_7</mi><mo>,</mo><mi>n_8</mi><mo>,</mo><mi>n_9</mi><mo>,</mo><mi>n_10</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3.</mn><mo>,</mo><mn>5.</mn><mo>,</mo><mn>6.</mn><mo>,</mo><mn>7.</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Mira quins valors són els més freqüents

]]> 1.6.2.22Q Moda10valors  Determina la moda de les notes següents:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»7«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»10«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«/mstyle»«/math»

 

Format: 5 (si no és única escriu les modes {22,24})

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_7</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_8</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_9</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_10</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>n_1</mi><mo>=</mo><mi>n_7</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>n_4</mi><mo>=</mo><mi>n_6</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>compta_element</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>n_1</mi><mo>,</mo><mi>n_2</mi><mo>,</mo><mi>n_3</mi><mo>,</mo><mi>n_4</mi><mo>,</mo><mi>n_5</mi><mo>,</mo><mi>n_6</mi><mo>,</mo><mi>n_7</mi><mo>,</mo><mi>n_8</mi><mo>,</mo><mi>n_9</mi><mo>,</mo><mi>n_10</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>n_1</mi><mo>,</mo><mi>n_2</mi><mo>,</mo><mi>n_3</mi><mo>,</mo><mi>n_4</mi><mo>,</mo><mi>n_5</mi><mo>,</mo><mi>n_6</mi><mo>,</mo><mi>n_7</mi><mo>,</mo><mi>n_8</mi><mo>,</mo><mi>n_9</mi><mo>,</mo><mi>n_10</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>moda</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi><mo>,</mo><mi>n_2</mi><mo>,</mo><mi>n_3</mi><mo>,</mo><mi>n_4</mi><mo>,</mo><mi>n_5</mi><mo>,</mo><mi>n_6</mi><mo>,</mo><mi>n_7</mi><mo>,</mo><mi>n_8</mi><mo>,</mo><mi>n_9</mi><mo>,</mo><mi>n_10</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3.</mn><mo>,</mo><mn>5.</mn><mo>,</mo><mn>6.</mn><mo>,</mo><mn>7.</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Mira quins valors són els més freqüents

]]> 1.6.2.25Q ModaTaula Quina és la moda d'aquesta distribució?

Xi Fi
#x_1 #n_1
#x_2 #n_2
#x_3 #n_3
#x_4 #n_4
#x_5 #n_5
#x_6 #n_6


5, si n'hi ha més d'una, format {2,3,5}

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>21</mn><mo>,</mo><mn>31</mn><mo>,</mo><mn>41</mn><mo>,</mo><mn>51</mn><mo>,</mo><mn>61</mn><mo>,</mo><mn>71</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_2</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_3</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_4</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_5</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_6</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mi>n_1</mi><mo>+</mo><mi>n_2</mi><mo>+</mo><mi>n_3</mi><mo>+</mo><mi>n_4</mi><mo>+</mo><mi>n_5</mi><mo>+</mo><mi>n_6</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mo>(</mo><mi>s</mi><mo> </mo><mi>mod</mi><mo> </mo><mn>10</mn><mo>)</mo><mo>=</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>n_1</mi><mo>≠</mo><mi>n_5</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>x_1</mi><mo>→</mo><mi>n_1</mi><mo>,</mo><mi>x_2</mi><mo>→</mo><mi>n_2</mi><mo>,</mo><mi>x_3</mi><mo>→</mo><mi>n_3</mi><mo>,</mo><mi>x_4</mi><mo>→</mo><mi>n_4</mi><mo>,</mo><mi>x_5</mi><mo>→</mo><mi>n_5</mi><mo>,</mo><mi>x_6</mi><mo>→</mo><mi>n_6</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>moda</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1.6.2.26Q ModaTaula Quina és la moda d'aquesta distribució?

Xi Fi
#x_1 #n_1
#x_2 #n_2
#x_3 #n_3
#x_4 #n_4
#x_5 #n_5
#x_6 #n_6


5, si n'hi ha més d'una, format {2,3,5}

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>21</mn><mo>,</mo><mn>31</mn><mo>,</mo><mn>41</mn><mo>,</mo><mn>51</mn><mo>,</mo><mn>61</mn><mo>,</mo><mn>71</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_2</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_3</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_4</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_5</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_6</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mi>n_1</mi><mo>+</mo><mi>n_2</mi><mo>+</mo><mi>n_3</mi><mo>+</mo><mi>n_4</mi><mo>+</mo><mi>n_5</mi><mo>+</mo><mi>n_6</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mo>(</mo><mi>s</mi><mo> </mo><mi>mod</mi><mo> </mo><mn>10</mn><mo>)</mo><mo>=</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>n_1</mi><mo>≠</mo><mi>n_5</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>x_1</mi><mo>→</mo><mi>n_1</mi><mo>,</mo><mi>x_2</mi><mo>→</mo><mi>n_2</mi><mo>,</mo><mi>x_3</mi><mo>→</mo><mi>n_3</mi><mo>,</mo><mi>x_4</mi><mo>→</mo><mi>n_4</mi><mo>,</mo><mi>x_5</mi><mo>→</mo><mi>n_5</mi><mo>,</mo><mi>x_6</mi><mo>→</mo><mi>n_6</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>moda</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1.6.2.30DT Mediana  

Mediana
És el valor de la variable xi que queda en el centre de la distribució:
  • si queda un sol valor o queden dos valors iguals de xi, aquest és la mediana.
  • si queden dos valors diferents de xi, es fa la seva mitjana aritmètica.

Amb una taula, pot ser útil calcular la freqüència acumulada.
]]> 0.0000000 0.0000000 0 1.6.2.31Q Mediana10valors  Determina la mediana de les notes següents:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»7«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»10«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«/mstyle»«/math»

 



Format: 5

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_7</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_8</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_9</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_10</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>ordena</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>n_1</mi><mo>,</mo><mi>n_2</mi><mo>,</mo><mi>n_3</mi><mo>,</mo><mi>n_4</mi><mo>,</mo><mi>n_5</mi><mo>,</mo><mi>n_6</mi><mo>,</mo><mi>n_7</mi><mo>,</mo><mi>n_8</mi><mo>,</mo><mi>n_9</mi><mo>,</mo><mi>n_10</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>mediana</mi><mo>(</mo><mi>R</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi><mo>,</mo><mi>n_2</mi><mo>,</mo><mi>n_3</mi><mo>,</mo><mi>n_4</mi><mo>,</mo><mi>n_5</mi><mo>,</mo><mi>n_6</mi><mo>,</mo><mi>n_7</mi><mo>,</mo><mi>n_8</mi><mo>,</mo><mi>n_9</mi><mo>,</mo><mi>n_10</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>10</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>10</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ordena les notes per saber quina és la que en té tantes per sota com per sobre.

]]> 1.6.2.32Q Mediana10valors  Determina la mediana de les notes següents:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»7«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»n_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»10«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨».«/mo»«/mstyle»«/math»

 



Format: 5

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_7</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_8</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_9</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_10</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>ordena</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>n_1</mi><mo>,</mo><mi>n_2</mi><mo>,</mo><mi>n_3</mi><mo>,</mo><mi>n_4</mi><mo>,</mo><mi>n_5</mi><mo>,</mo><mi>n_6</mi><mo>,</mo><mi>n_7</mi><mo>,</mo><mi>n_8</mi><mo>,</mo><mi>n_9</mi><mo>,</mo><mi>n_10</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>mediana</mi><mo>(</mo><mi>R</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi><mo>,</mo><mi>n_2</mi><mo>,</mo><mi>n_3</mi><mo>,</mo><mi>n_4</mi><mo>,</mo><mi>n_5</mi><mo>,</mo><mi>n_6</mi><mo>,</mo><mi>n_7</mi><mo>,</mo><mi>n_8</mi><mo>,</mo><mi>n_9</mi><mo>,</mo><mi>n_10</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>10</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>10</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ordena les notes per saber quina és la que en té tantes per sota com per sobre.

]]> 1.6.2.35Q MedianaTaula Quina és la mediana d'aquesta distribució?

Xi Fi
#x_1 #n_1
#x_2 #n_2
#x_3 #n_3
#x_4 #n_4
#x_5 #n_5
#x_6 #n_6




]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>21</mn><mo>,</mo><mn>31</mn><mo>,</mo><mn>41</mn><mo>,</mo><mn>51</mn><mo>,</mo><mn>61</mn><mo>,</mo><mn>71</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_2</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_3</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_4</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_5</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_6</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mi>n_1</mi><mo>+</mo><mi>n_2</mi><mo>+</mo><mi>n_3</mi><mo>+</mo><mi>n_4</mi><mo>+</mo><mi>n_5</mi><mo>+</mo><mi>n_6</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mo>(</mo><mi>s</mi><mo> </mo><mi>mod</mi><mo> </mo><mn>10</mn><mo>)</mo><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi><mo>=</mo><mi>n_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi><mo>=</mo><mi>t_1</mi><mo>+</mo><mi>n_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_3</mi><mo>=</mo><mi>t_2</mi><mo>+</mo><mi>n_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_4</mi><mo>=</mo><mi>t_3</mi><mo>+</mo><mi>n_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_5</mi><mo>=</mo><mi>t_4</mi><mo>+</mo><mi>n_5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_6</mi><mo>=</mo><mi>t_5</mi><mo>+</mo><mi>n_6</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>x_1</mi><mo>→</mo><mi>n_1</mi><mo>,</mo><mi>x_2</mi><mo>→</mo><mi>n_2</mi><mo>,</mo><mi>x_3</mi><mo>→</mo><mi>n_3</mi><mo>,</mo><mi>x_4</mi><mo>→</mo><mi>n_4</mi><mo>,</mo><mi>x_5</mi><mo>→</mo><mi>n_5</mi><mo>,</mo><mi>x_6</mi><mo>→</mo><mi>n_6</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>mediana</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Pots calcular les freqüències acumulades per saber quin és el valor de la mediana:

Fi Fi FA
#x_1 #n_1 #t_1
#x_2 #n_2 #t_2
#x_3 #n_3 #t_3
#x_4 #n_4 #t_4
#x_5 #n_5 #t_5
#x_6 #n_6 #t_6
Total #s  




]]> 1.6.2.36Q MedianaTaula Quina és la mediana d'aquesta distribució?

Xi Fi
#x_1 #n_1
#x_2 #n_2
#x_3 #n_3
#x_4 #n_4
#x_5 #n_5
#x_6 #n_6




]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>21</mn><mo>,</mo><mn>31</mn><mo>,</mo><mn>41</mn><mo>,</mo><mn>51</mn><mo>,</mo><mn>61</mn><mo>,</mo><mn>71</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_2</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_3</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_4</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_5</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_6</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mi>n_1</mi><mo>+</mo><mi>n_2</mi><mo>+</mo><mi>n_3</mi><mo>+</mo><mi>n_4</mi><mo>+</mo><mi>n_5</mi><mo>+</mo><mi>n_6</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mo>(</mo><mi>s</mi><mo> </mo><mi>mod</mi><mo> </mo><mn>10</mn><mo>)</mo><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi><mo>=</mo><mi>n_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi><mo>=</mo><mi>t_1</mi><mo>+</mo><mi>n_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_3</mi><mo>=</mo><mi>t_2</mi><mo>+</mo><mi>n_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_4</mi><mo>=</mo><mi>t_3</mi><mo>+</mo><mi>n_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_5</mi><mo>=</mo><mi>t_4</mi><mo>+</mo><mi>n_5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_6</mi><mo>=</mo><mi>t_5</mi><mo>+</mo><mi>n_6</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>x_1</mi><mo>→</mo><mi>n_1</mi><mo>,</mo><mi>x_2</mi><mo>→</mo><mi>n_2</mi><mo>,</mo><mi>x_3</mi><mo>→</mo><mi>n_3</mi><mo>,</mo><mi>x_4</mi><mo>→</mo><mi>n_4</mi><mo>,</mo><mi>x_5</mi><mo>→</mo><mi>n_5</mi><mo>,</mo><mi>x_6</mi><mo>→</mo><mi>n_6</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>mediana</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Pots calcular les freqüències acumulades per saber quin és el valor de la mediana:

Fi Fi FA
#x_1 #n_1 #t_1
#x_2 #n_2 #t_2
#x_3 #n_3 #t_3
#x_4 #n_4 #t_4
#x_5 #n_5 #t_5
#x_6 #n_6 #t_6
Total #s  




]]> 1.6.2.50DT Desviació mitjana  

Desviació mitjana
És la mitjana de les desviacions i es calcula amb
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi mathvariant=¨bold¨»d«/mi»«mo».«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo».«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«munderover»«mo»§#8721;«/mo»«mrow»«mi mathvariant=¨bold¨»i«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mi mathvariant=¨bold¨»j«/mi»«/munderover»«mo»|«/mo»«mover»«mi mathvariant=¨bold¨»x«/mi»«mo»§#175;«/mo»«/mover»«mo»-«/mo»«msub»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»i«/mi»«/msub»«mo»|«/mo»«mo»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»f«/mi»«mi mathvariant=¨bold¨»i«/mi»«/msub»«/mrow»«/mstyle»«/math»
]]> 0.0000000 0.0000000 0 1.6.2.51Q DesviacióMitjanaTaula A partir de les dades següents

Xi Fi
#x_1 #n_1
#x_2 #n_2
#x_3 #n_3
#x_4 #n_4
#x_5 #n_5
#x_6 #n_6
TOTAL #s


Determina la mitjana i la desviació mitjana.
Arrodoneix als centèsims.

]]> 1.0000000 0.5000000 0 0 a) Mitjana =#sol1b) d.m. =#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>21</mn><mo>,</mo><mn>31</mn><mo>,</mo><mn>41</mn><mo>,</mo><mn>51</mn><mo>,</mo><mn>61</mn><mo>,</mo><mn>71</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_2</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_3</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_4</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_5</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_6</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mi>n_1</mi><mo>+</mo><mi>n_2</mi><mo>+</mo><mi>n_3</mi><mo>+</mo><mi>n_4</mi><mo>+</mo><mi>n_5</mi><mo>+</mo><mi>n_6</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mo>(</mo><mi>s</mi><mo> </mo><mi>mod</mi><mo> </mo><mn>10</mn><mo>)</mo><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_1</mi><mo>=</mo><mfrac><mi>n_1</mi><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_2</mi><mo>=</mo><mfrac><mi>n_2</mi><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_3</mi><mo>=</mo><mfrac><mi>n_3</mi><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_4</mi><mo>=</mo><mfrac><mi>n_4</mi><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_5</mi><mo>=</mo><mfrac><mi>n_5</mi><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_6</mi><mo>=</mo><mfrac><mi>n_6</mi><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mi>x_1</mi><mo>*</mo><mi>f_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mi>x_2</mi><mo>*</mo><mi>f_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi><mo>=</mo><mi>x_3</mi><mo>*</mo><mi>f_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_4</mi><mo>=</mo><mi>x_4</mi><mo>*</mo><mi>f_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_5</mi><mo>=</mo><mi>x_5</mi><mo>*</mo><mi>f_5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_6</mi><mo>=</mo><mi>x_6</mi><mo>*</mo><mi>f_6</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_1</mi><mo>=</mo><mi>r_1</mi><mo>+</mo><mi>r_2</mi><mo>+</mo><mi>r_3</mi><mo>+</mo><mi>r_4</mi><mo>+</mo><mi>r_5</mi><mo>+</mo><mi>r_6</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>m_1</mi><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>m</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_1</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>m</mi><mo>-</mo><mi>x_1</mi></mrow></mfenced><mo>*</mo><mi>f_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_2</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>m</mi><mo>-</mo><mi>x_2</mi></mrow></mfenced><mo>*</mo><mi>f_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_3</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>m</mi><mo>-</mo><mi>x_3</mi></mrow></mfenced><mo>*</mo><mi>f_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_4</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>m</mi><mo>-</mo><mi>x_4</mi></mrow></mfenced><mo>*</mo><mi>f_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_5</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>m</mi><mo>-</mo><mi>x_5</mi></mrow></mfenced><mo>*</mo><mi>f_5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_6</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>m</mi><mo>-</mo><mi>x_6</mi></mrow></mfenced><mo>*</mo><mi>f_6</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>d_1</mi><mo>+</mo><mi>d_2</mi><mo>+</mo><mi>d_3</mi><mo>+</mo><mi>d_4</mi><mo>+</mo><mi>d_5</mi><mo>+</mo><mi>d_6</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>d</mi><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerància</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi><mo>,</mo><mi>x_2</mi><mo>,</mo><mi>x_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>71</mn><mo>,</mo><mn>72</mn><mo>,</mo><mn>73</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi><mo>,</mo><mi>n_2</mi><mo>,</mo><mi>n_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>,</mo><mn>12</mn><mo>,</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1477</mn><mn>20</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>73.85</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.565</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.57</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo>&#x000A0;</mo><mi>M</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi mathvariant="normal">j</mi><mi>a</mi><mi>n</mi><mi>a</mi><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#x000A0;</mo><mi mathvariant="normal">d</mi><mo>.</mo><mi>m</mi><mo>.</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Fes-ho amb Excel

]]> 1.6.2.52Q DesviacióMitjanaTaula_2 A partir de les dades següents

Xi Fi
#x_1 #n_1
#x_2 #n_2
#x_3 #n_3
#x_4 #n_4
#x_5 #n_5
#x_6 #n_6
TOTAL #s


Determina la mitjana i la desviació mitjana.
Arrodoneix als centèsims.

]]> 1.0000000 0.5000000 0 0 a) Mitjana =#sol1b) d.m. =#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>21</mn><mo>,</mo><mn>31</mn><mo>,</mo><mn>41</mn><mo>,</mo><mn>51</mn><mo>,</mo><mn>61</mn><mo>,</mo><mn>71</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_2</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_3</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_4</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_5</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_6</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mi>n_1</mi><mo>+</mo><mi>n_2</mi><mo>+</mo><mi>n_3</mi><mo>+</mo><mi>n_4</mi><mo>+</mo><mi>n_5</mi><mo>+</mo><mi>n_6</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mo>(</mo><mi>s</mi><mo> </mo><mi>mod</mi><mo> </mo><mn>10</mn><mo>)</mo><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_1</mi><mo>=</mo><mfrac><mi>n_1</mi><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_2</mi><mo>=</mo><mfrac><mi>n_2</mi><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_3</mi><mo>=</mo><mfrac><mi>n_3</mi><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_4</mi><mo>=</mo><mfrac><mi>n_4</mi><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_5</mi><mo>=</mo><mfrac><mi>n_5</mi><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_6</mi><mo>=</mo><mfrac><mi>n_6</mi><mi>s</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mi>x_1</mi><mo>*</mo><mi>f_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mi>x_2</mi><mo>*</mo><mi>f_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi><mo>=</mo><mi>x_3</mi><mo>*</mo><mi>f_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_4</mi><mo>=</mo><mi>x_4</mi><mo>*</mo><mi>f_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_5</mi><mo>=</mo><mi>x_5</mi><mo>*</mo><mi>f_5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_6</mi><mo>=</mo><mi>x_6</mi><mo>*</mo><mi>f_6</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_1</mi><mo>=</mo><mi>r_1</mi><mo>+</mo><mi>r_2</mi><mo>+</mo><mi>r_3</mi><mo>+</mo><mi>r_4</mi><mo>+</mo><mi>r_5</mi><mo>+</mo><mi>r_6</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>m_1</mi><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>m</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_1</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>m</mi><mo>-</mo><mi>x_1</mi></mrow></mfenced><mo>*</mo><mi>f_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_2</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>m</mi><mo>-</mo><mi>x_2</mi></mrow></mfenced><mo>*</mo><mi>f_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_3</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>m</mi><mo>-</mo><mi>x_3</mi></mrow></mfenced><mo>*</mo><mi>f_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_4</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>m</mi><mo>-</mo><mi>x_4</mi></mrow></mfenced><mo>*</mo><mi>f_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_5</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>m</mi><mo>-</mo><mi>x_5</mi></mrow></mfenced><mo>*</mo><mi>f_5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_6</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>m</mi><mo>-</mo><mi>x_6</mi></mrow></mfenced><mo>*</mo><mi>f_6</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>d_1</mi><mo>+</mo><mi>d_2</mi><mo>+</mo><mi>d_3</mi><mo>+</mo><mi>d_4</mi><mo>+</mo><mi>d_5</mi><mo>+</mo><mi>d_6</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>d</mi><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi><mo>,</mo><mi>x_2</mi><mo>,</mo><mi>x_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>71</mn><mo>,</mo><mn>72</mn><mo>,</mo><mn>73</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi><mo>,</mo><mi>n_2</mi><mo>,</mo><mi>n_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>,</mo><mn>12</mn><mo>,</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1477</mn><mn>20</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>73.85</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.565</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.57</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo>&#x000A0;</mo><mi>M</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi mathvariant="normal">j</mi><mi>a</mi><mi>n</mi><mi>a</mi><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#x000A0;</mo><mi mathvariant="normal">d</mi><mo>.</mo><mi>m</mi><mo>.</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Fes-ho amb Excel

]]> 1.6.2.70DT Desviació típica  

Desviació típica
La variància és la mitjana dels quadrats de les desviacions i es calcula amb
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#003300¨»«mi mathcolor=¨#003300¨»§#963;«/mi»«mn»2«/mn»«/msup»«mo mathcolor=¨#003300¨»§#160;«/mo»«mo mathcolor=¨#003300¨»=«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«munderover mathcolor=¨#003300¨»«mrow»«mo»§#8721;«/mo»«mo»(«/mo»«/mrow»«mrow»«mi mathvariant=¨bold¨»i«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mi mathvariant=¨bold¨»j«/mi»«/munderover»«mover mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»x«/mi»«mo»§#175;«/mo»«/mover»«mo mathcolor=¨#003300¨»-«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mi mathvariant=¨bold¨»i«/mi»«/msub»«msup mathcolor=¨#003300¨»«mo»)«/mo»«mn»2«/mn»«/msup»«mo mathcolor=¨#003300¨»§#183;«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»f«/mi»«mi mathvariant=¨bold¨»i«/mi»«/msub»«/math»

La desviació típica és l'arrel de la variància:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathcolor=¨#003300¨»§#963;«/mi»«mo mathcolor=¨#003300¨»§#160;«/mo»«mo mathcolor=¨#003300¨»=«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«msqrt mathcolor=¨#003300¨»«munderover»«mo»§#8721;«/mo»«mrow»«mi»i«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mi»j«/mi»«/munderover»«mo»(«/mo»«mover»«mi»x«/mi»«mo»§#175;«/mo»«/mover»«mo»-«/mo»«msub»«mi»x«/mi»«mi»i«/mi»«/msub»«msup»«mo»)«/mo»«mn»2«/mn»«/msup»«mo»§#183;«/mo»«msub»«mi»f«/mi»«mi»i«/mi»«/msub»«/msqrt»«/math»
]]> 0.0000000 0.0000000 0 1.6.2.71Q DesviacióTípicaTaula A partir de la taula

Xi Fi
#x_1 #n_1
#x_2 #n_2
#x_3 #n_3
#x_4 #n_4
#x_5 #n_5
#x_6 #n_6
TOTAL =#s


Determina la  mitjana i la desviació típica (és l'arrel de la variància).

Arrodoneix tots els resultats als centèsims.

 

]]> 1.0000000 0.5000000 0 0 a) Mitjana=#sol1b) σ =#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>21</mn><mo>,</mo><mn>31</mn><mo>,</mo><mn>41</mn><mo>,</mo><mn>51</mn><mo>,</mo><mn>61</mn><mo>,</mo><mn>71</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_2</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_3</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_4</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_5</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_6</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mi>n_1</mi><mo>+</mo><mi>n_2</mi><mo>+</mo><mi>n_3</mi><mo>+</mo><mi>n_4</mi><mo>+</mo><mi>n_5</mi><mo>+</mo><mi>n_6</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mo>(</mo><mi>s</mi><mo> </mo><mi>mod</mi><mo> </mo><mn>10</mn><mo>)</mo><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_1</mi><mo>=</mo><mfrac><mi>n_1</mi><mi>s</mi></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_2</mi><mo>=</mo><mfrac><mi>n_2</mi><mi>s</mi></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_3</mi><mo>=</mo><mfrac><mi>n_3</mi><mi>s</mi></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_4</mi><mo>=</mo><mfrac><mi>n_4</mi><mi>s</mi></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_5</mi><mo>=</mo><mfrac><mi>n_5</mi><mi>s</mi></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_6</mi><mo>=</mo><mfrac><mi>n_6</mi><mi>s</mi></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mi>x_1</mi><mo>*</mo><mi>f_1</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mi>x_2</mi><mo>*</mo><mi>f_2</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi><mo>=</mo><mi>x_3</mi><mo>*</mo><mi>f_3</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_4</mi><mo>=</mo><mi>x_4</mi><mo>*</mo><mi>f_4</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_5</mi><mo>=</mo><mi>x_5</mi><mo>*</mo><mi>f_5</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_6</mi><mo>=</mo><mi>x_6</mi><mo>*</mo><mi>f_6</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_1</mi><mo>=</mo><mi>r_1</mi><mo>+</mo><mi>r_2</mi><mo>+</mo><mi>r_3</mi><mo>+</mo><mi>r_4</mi><mo>+</mo><mi>r_5</mi><mo>+</mo><mi>r_6</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>m_1</mi><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_1</mi><mo>=</mo><msup><mfenced><mfenced close="|" open="|"><mrow><mi>m</mi><mo>-</mo><mi>x_1</mi></mrow></mfenced></mfenced><mn>2</mn></msup><mo>*</mo><mi>f_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_2</mi><mo>=</mo><msup><mfenced><mfenced close="|" open="|"><mrow><mi>m</mi><mo>-</mo><mi>x_2</mi></mrow></mfenced></mfenced><mn>2</mn></msup><mo>*</mo><mi>f_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_3</mi><mo>=</mo><msup><mfenced><mfenced close="|" open="|"><mrow><mi>m</mi><mo>-</mo><mi>x_3</mi></mrow></mfenced></mfenced><mn>2</mn></msup><mo>*</mo><mi>f_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_4</mi><mo>=</mo><msup><mfenced><mfenced close="|" open="|"><mrow><mi>m</mi><mo>-</mo><mi>x_4</mi></mrow></mfenced></mfenced><mn>2</mn></msup><mo>*</mo><mi>f_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_5</mi><mo>=</mo><msup><mfenced><mfenced close="|" open="|"><mrow><mi>m</mi><mo>-</mo><mi>x_5</mi></mrow></mfenced></mfenced><mn>2</mn></msup><mo>*</mo><mi>f_5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_6</mi><mo>=</mo><msup><mfenced><mfenced close="|" open="|"><mrow><mi>m</mi><mo>-</mo><mi>x_6</mi></mrow></mfenced></mfenced><mn>2</mn></msup><mo>*</mo><mi>f_6</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mfenced><mrow><mn>100</mn><mo>*</mo><mfenced><msqrt><mrow><mi>d_1</mi><mo>+</mo><mi>d_2</mi><mo>+</mo><mi>d_3</mi><mo>+</mo><mi>d_4</mi><mo>+</mo><mi>d_5</mi><mo>+</mo><mi>d_6</mi></mrow></msqrt></mfenced></mrow></mfenced></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>x_1</mi><mo>→</mo><mi>n_1</mi><mo>,</mo><mi>x_2</mi><mo>→</mo><mi>n_2</mi><mo>,</mo><mi>x_3</mi><mo>→</mo><mi>n_3</mi><mo>,</mo><mi>x_4</mi><mo>→</mo><mi>n_4</mi><mo>,</mo><mi>x_5</mi><mo>→</mo><mi>n_5</mi><mo>,</mo><mi>x_6</mi><mo>→</mo><mi>n_6</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>variància_n</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><msqrt><mi>v</mi></msqrt><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>m</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>t</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerància</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi><mo>,</mo><mi>x_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>31</mn><mo>,</mo><mn>32</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi><mo>,</mo><mi>n_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>70</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>34.14</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.58</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo>&#x000A0;</mo><mi>M</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi mathvariant="normal">j</mi><mi>a</mi><mi>n</mi><mi>a</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#x02009;</mo><mi>&#x003C3;</mi><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Fes-ho amb Excel

 

Xi Fi fi xi · fi «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathcolor=¨#00007F¨»|«/mo»«mover mathcolor=¨#00007F¨»«mi»x«/mi»«mo»§#175;«/mo»«/mover»«mo mathcolor=¨#00007F¨»-«/mo»«msub mathcolor=¨#00007F¨»«mi mathcolor=¨#00007F¨»x«/mi»«mi»i«/mi»«/msub»«msup mathcolor=¨#00007F¨»«mo»|«/mo»«mn»2«/mn»«/msup»«mo mathcolor=¨#00007F¨»§#183;«/mo»«msub mathcolor=¨#00007F¨»«mi mathcolor=¨#00007F¨»f«/mi»«mi»i«/mi»«/msub»«/mrow»«/mstyle»«/math»
#x_1 #n_1 #f_1 #r_1 #d_1
#x_2 #n_2 #f_2 #r_2 #d_2
#x_3 #n_3 #f_3 #r_3 #d_3
#x_4 #n_4 #f_4 #r_4 #d_4
#x_5 #n_5 #f_5 #r_5 #d_5
#x_6 #n_6 #f_6 #r_6 #d_6
TOTAL #s 1    



]]> 1.6.2.72Q DesviacióTípicaTaula_2 A partir de la taula

Xi Fi
#x_1 #n_1
#x_2 #n_2
#x_3 #n_3
#x_4 #n_4
#x_5 #n_5
#x_6 #n_6
TOTAL =#s


Determina la  mitjana i la desviació típica.

Arrodoneix tots els resultats als centèsims.

 

]]> 1.0000000 0.5000000 0 0 a) Mitjana=#sol1b) σ =#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>100</mn><mo>,</mo><mn>200</mn><mo>,</mo><mn>300</mn><mo>,</mo><mn>400</mn><mo>,</mo><mn>500</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_2</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>10</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_3</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>20</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_4</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>30</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_5</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>40</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_6</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>50</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mi>n_1</mi><mo>+</mo><mi>n_2</mi><mo>+</mo><mi>n_3</mi><mo>+</mo><mi>n_4</mi><mo>+</mo><mi>n_5</mi><mo>+</mo><mi>n_6</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mo>(</mo><mi>s</mi><mo> </mo><mi>mod</mi><mo> </mo><mn>10</mn><mo>)</mo><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_1</mi><mo>=</mo><mfrac><mi>n_1</mi><mi>s</mi></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_2</mi><mo>=</mo><mfrac><mi>n_2</mi><mi>s</mi></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_3</mi><mo>=</mo><mfrac><mi>n_3</mi><mi>s</mi></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_4</mi><mo>=</mo><mfrac><mi>n_4</mi><mi>s</mi></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_5</mi><mo>=</mo><mfrac><mi>n_5</mi><mi>s</mi></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_6</mi><mo>=</mo><mfrac><mi>n_6</mi><mi>s</mi></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mi>x_1</mi><mo>*</mo><mi>f_1</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mi>x_2</mi><mo>*</mo><mi>f_2</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi><mo>=</mo><mi>x_3</mi><mo>*</mo><mi>f_3</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_4</mi><mo>=</mo><mi>x_4</mi><mo>*</mo><mi>f_4</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_5</mi><mo>=</mo><mi>x_5</mi><mo>*</mo><mi>f_5</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_6</mi><mo>=</mo><mi>x_6</mi><mo>*</mo><mi>f_6</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_1</mi><mo>=</mo><mi>r_1</mi><mo>+</mo><mi>r_2</mi><mo>+</mo><mi>r_3</mi><mo>+</mo><mi>r_4</mi><mo>+</mo><mi>r_5</mi><mo>+</mo><mi>r_6</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>m_1</mi><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_1</mi><mo>=</mo><msup><mfenced><mfenced close="|" open="|"><mrow><mi>m</mi><mo>-</mo><mi>x_1</mi></mrow></mfenced></mfenced><mn>2</mn></msup><mo>*</mo><mi>f_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_2</mi><mo>=</mo><msup><mfenced><mfenced close="|" open="|"><mrow><mi>m</mi><mo>-</mo><mi>x_2</mi></mrow></mfenced></mfenced><mn>2</mn></msup><mo>*</mo><mi>f_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_3</mi><mo>=</mo><msup><mfenced><mfenced close="|" open="|"><mrow><mi>m</mi><mo>-</mo><mi>x_3</mi></mrow></mfenced></mfenced><mn>2</mn></msup><mo>*</mo><mi>f_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_4</mi><mo>=</mo><msup><mfenced><mfenced close="|" open="|"><mrow><mi>m</mi><mo>-</mo><mi>x_4</mi></mrow></mfenced></mfenced><mn>2</mn></msup><mo>*</mo><mi>f_4</mi></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>x_1</mi><mo>→</mo><mi>n_1</mi><mo>,</mo><mi>x_2</mi><mo>→</mo><mi>n_2</mi><mo>,</mo><mi>x_3</mi><mo>→</mo><mi>n_3</mi><mo>,</mo><mi>x_4</mi><mo>→</mo><mi>n_4</mi><mo>,</mo><mi>x_5</mi><mo>→</mo><mi>n_5</mi><mo>,</mo><mi>x_6</mi><mo>→</mo><mi>n_6</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>variància_n</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><msqrt><mi>v</mi></msqrt><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>m</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>t</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerància</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi><mo>,</mo><mi>x_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>400</mn><mo>,</mo><mn>410</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi><mo>,</mo><mi>n_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>422.6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>19.16</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo>&#x000A0;</mo><mi>M</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi mathvariant="normal">j</mi><mi>a</mi><mi>n</mi><mi>a</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#x02009;</mo><mi>&#x003C3;</mi><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Fes-ho amb Excel

 

Xi Fi fi xi · fi «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathcolor=¨#00007F¨»|«/mo»«mover mathcolor=¨#00007F¨»«mi»x«/mi»«mo»§#175;«/mo»«/mover»«mo mathcolor=¨#00007F¨»-«/mo»«msub mathcolor=¨#00007F¨»«mi mathcolor=¨#00007F¨»x«/mi»«mi»i«/mi»«/msub»«msup mathcolor=¨#00007F¨»«mo»|«/mo»«mn»2«/mn»«/msup»«mo mathcolor=¨#00007F¨»§#183;«/mo»«msub mathcolor=¨#00007F¨»«mi mathcolor=¨#00007F¨»f«/mi»«mi»i«/mi»«/msub»«/mrow»«/mstyle»«/math»
#x_1 #n_1 #f_1 #r_1 #d_1
#x_2 #n_2 #f_2 #r_2 #d_2
#x_3 #n_3 #f_3 #r_3 #d_3
#x_4 #n_4 #f_4 #r_4 #d_4
#x_5 #n_5 #f_5 #r_5 #d_5
#x_6 #n_6 #f_6 #r_6 #d_6
TOTAL #s 1    



]]> 1.6.2.73Q DesvTipSab En una sabateria, s'han venut parells de sabates de les talles indicades per Xi en quantitats precisades en la columna Fi. Determina quina és la mitjana de les talles i quina és la desviació típica de les ventes respecte a aquesta mitjana.

Xi Fi
#x_1 #n_1
#x_2 #n_2
#x_3 #n_3
#x_4 #n_4
#x_5 #n_5
#x_6 #n_6
TOTAL =#s
 
Arrodoneix tots els resultats als centèsims.

 

]]> 1.0000000 0.5000000 0 0 a) Mitjana=#sol1b) σ =#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>34</mn><mo>,</mo><mn>37</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_2</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_3</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_4</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_5</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_6</mi><mo>=</mo><mi>x_1</mi><mo>+</mo><mn>7</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mi>n_1</mi><mo>+</mo><mi>n_2</mi><mo>+</mo><mi>n_3</mi><mo>+</mo><mi>n_4</mi><mo>+</mo><mi>n_5</mi><mo>+</mo><mi>n_6</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mo>(</mo><mi>s</mi><mo> </mo><mi>mod</mi><mo> </mo><mn>10</mn><mo>)</mo><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_1</mi><mo>=</mo><mfrac><mi>n_1</mi><mi>s</mi></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_2</mi><mo>=</mo><mfrac><mi>n_2</mi><mi>s</mi></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_3</mi><mo>=</mo><mfrac><mi>n_3</mi><mi>s</mi></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_4</mi><mo>=</mo><mfrac><mi>n_4</mi><mi>s</mi></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_5</mi><mo>=</mo><mfrac><mi>n_5</mi><mi>s</mi></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_6</mi><mo>=</mo><mfrac><mi>n_6</mi><mi>s</mi></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mi>x_1</mi><mo>*</mo><mi>f_1</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mi>x_2</mi><mo>*</mo><mi>f_2</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi><mo>=</mo><mi>x_3</mi><mo>*</mo><mi>f_3</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_4</mi><mo>=</mo><mi>x_4</mi><mo>*</mo><mi>f_4</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_5</mi><mo>=</mo><msup><mfenced><mfenced close="|" open="|"><mrow><mi>m</mi><mo>-</mo><mi>x_5</mi></mrow></mfenced></mfenced><mn>2</mn></msup><mo>*</mo><mi>f_5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_6</mi><mo>=</mo><msup><mfenced><mfenced close="|" open="|"><mrow><mi>m</mi><mo>-</mo><mi>x_6</mi></mrow></mfenced></mfenced><mn>2</mn></msup><mo>*</mo><mi>f_6</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mfenced><mrow><mn>100</mn><mo>*</mo><mfenced><msqrt><mrow><mi>d_1</mi><mo>+</mo><mi>d_2</mi><mo>+</mo><mi>d_3</mi><mo>+</mo><mi>d_4</mi><mo>+</mo><mi>d_5</mi><mo>+</mo><mi>d_6</mi></mrow></msqrt></mfenced></mrow></mfenced></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>x_1</mi><mo>→</mo><mi>n_1</mi><mo>,</mo><mi>x_2</mi><mo>→</mo><mi>n_2</mi><mo>,</mo><mi>x_3</mi><mo>→</mo><mi>n_3</mi><mo>,</mo><mi>x_4</mi><mo>→</mo><mi>n_4</mi><mo>,</mo><mi>x_5</mi><mo>→</mo><mi>n_5</mi><mo>,</mo><mi>x_6</mi><mo>→</mo><mi>n_6</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>variància_n</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><msqrt><mi>v</mi></msqrt><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>m</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>t</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerància</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi><mo>,</mo><mi>x_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>34</mn><mo>,</mo><mn>35</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi><mo>,</mo><mi>n_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>,</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>70</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>37.64</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2.27</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo>&#xA0;</mo><mi>M</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi mathvariant="normal">j</mi><mi>a</mi><mi>n</mi><mi>a</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#x2009;</mo><mi>&#x3C3;</mi><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Fes-ho amb Excel

 

Xi Fi fi xi · fi «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathcolor=¨#00007F¨»|«/mo»«mover mathcolor=¨#00007F¨»«mi»x«/mi»«mo»§#175;«/mo»«/mover»«mo mathcolor=¨#00007F¨»-«/mo»«msub mathcolor=¨#00007F¨»«mi mathcolor=¨#00007F¨»x«/mi»«mi»i«/mi»«/msub»«msup mathcolor=¨#00007F¨»«mo»|«/mo»«mn»2«/mn»«/msup»«mo mathcolor=¨#00007F¨»§#183;«/mo»«msub mathcolor=¨#00007F¨»«mi mathcolor=¨#00007F¨»f«/mi»«mi»i«/mi»«/msub»«/mrow»«/mstyle»«/math»
#x_1 #n_1 #f_1 #r_1 #d_1
#x_2 #n_2 #f_2 #r_2 #d_2
#x_3 #n_3 #f_3 #r_3 #d_3
#x_4 #n_4 #f_4 #r_4 #d_4
#x_5 #n_5 #f_5 #r_5 #d_5
#x_6 #n_6 #f_6 #r_6 #d_6
TOTAL #s 1    



]]> 1rBTX 06. ESTADÍSTICA/1.6.3 Bidimensional 1.6.3.10DT Covariància  

Covariància
La covariància és la mitjana dels productes de les desviacions de Xi i de Yi respecte a les seves mitjanes. Es calcula amb:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#963;«/mi»«mi mathvariant=¨bold¨»XY«/mi»«/msub»«mo mathcolor=¨#003300¨»§#160;«/mo»«mo mathcolor=¨#003300¨»=«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«munderover mathcolor=¨#003300¨»«mo»§#8721;«/mo»«mrow»«mi mathvariant=¨bold¨»i«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mi mathvariant=¨bold¨»n«/mi»«/munderover»«mfenced mathcolor=¨#003300¨»«mrow»«mover»«mi mathvariant=¨bold¨»X«/mi»«mo»§#175;«/mo»«/mover»«mo»-«/mo»«msub»«mi mathvariant=¨bold¨»X«/mi»«mi mathvariant=¨bold¨»i«/mi»«/msub»«/mrow»«/mfenced»«mo mathcolor=¨#003300¨»§#183;«/mo»«mfenced mathcolor=¨#003300¨»«mrow»«mover»«mi mathvariant=¨bold¨»Y«/mi»«mo»§#175;«/mo»«/mover»«mo»-«/mo»«msub»«mi mathvariant=¨bold¨»Y«/mi»«mi mathvariant=¨bold¨»i«/mi»«/msub»«/mrow»«/mfenced»«mo mathcolor=¨#003300¨»§#183;«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»f«/mi»«mi mathvariant=¨bold¨»i«/mi»«/msub»«/math»
]]> 0.0000000 0.0000000 0 1.6.3.11Q CovarSenseFreqüències S'estudia la relació entre les hores d'insolació (Xi) i la producció d'una mostra de presseguers, amb els resultats següents:

Xi

Yi

#x1

#y1

#x2

#y2

#x3

#y3

#x4

#y4

#x5

#y5

Arrodoneix als centèsims els resultats de l'Excel i no posis unitats

a) Calcula la mitjana d'hores d'insolació:
b) Calcula la mitjana de la producció de fruits:
c) Calcula la covariància

]]> 1.0000000 0.3333333 0 0 a) X¯=#hb) Y¯=#nc) σXY=#c]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mn>100</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mn>20</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>=</mo><mi>x2</mi><mo>+</mo><mn>20</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x4</mi><mo>=</mo><mi>x3</mi><mo>+</mo><mn>20</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x5</mi><mo>=</mo><mi>x4</mi><mo>+</mo><mn>20</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>y1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>12</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>12</mn><mo>,</mo><mn>16</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>15</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>18</mn><mo>,</mo><mn>24</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>28</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mi>x3</mi><mo>,</mo><mi>x4</mi><mo>,</mo><mi>x5</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y1</mi><mo>,</mo><mi>y2</mi><mo>,</mo><mi>y3</mi><mo>,</mo><mi>y4</mi><mo>,</mo><mi>y5</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>mitjana</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>mitjana</mi><mo>(</mo><mi>Y</mi><mo>)</mo><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mfenced><mrow><mo>(</mo><mn>100</mn><mo>*</mo><mo>(</mo><mi>x1</mi><mo>-</mo><mi>h</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y1</mi><mo>-</mo><mi>n</mi><mo>)</mo></mrow></mfenced><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mfenced><mrow><mo>(</mo><mn>100</mn><mo>*</mo><mo>(</mo><mi>x2</mi><mo>-</mo><mi>h</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y2</mi><mo>-</mo><mi>n</mi><mo>)</mo><mo>)</mo></mrow></mfenced></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mfenced><mrow><mo>(</mo><mn>100</mn><mo>*</mo><mo>(</mo><mi>x3</mi><mo>-</mo><mi>h</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y3</mi><mo>-</mo><mi>n</mi><mo>)</mo></mrow></mfenced><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t4</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mfenced><mrow><mo>(</mo><mn>100</mn><mo>*</mo><mo>(</mo><mi>x4</mi><mo>-</mo><mi>h</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y4</mi><mo>-</mo><mi>n</mi><mo>)</mo><mo>)</mo></mrow></mfenced></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t5</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mfenced><mrow><mo>(</mo><mn>100</mn><mo>*</mo><mo>(</mo><mi>x5</mi><mo>-</mo><mi>h</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y5</mi><mo>-</mo><mi>n</mi><mo>)</mo><mo>)</mo></mrow></mfenced></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mfenced><mrow><mi>t1</mi><mo>+</mo><mi>t2</mi><mo>+</mo><mi>t3</mi><mo>+</mo><mi>t4</mi><mo>+</mo><mi>t5</mi></mrow></mfenced><mo>/</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerància</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>,</mo><mi>Y</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>200</mn><mo>,</mo><mn>220</mn><mo>,</mo><mn>240</mn><mo>,</mo><mn>260</mn><mo>,</mo><mn>280</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>10</mn><mo>,</mo><mn>15</mn><mo>,</mo><mn>19</mn><mo>,</mo><mn>23</mn><mo>,</mo><mn>24</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>,</mo><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>240.</mn><mo>,</mo><mn>18.2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>144.</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:wrs="http://www.wiris.com/xml/mathml-extension"><mi>a</mi><mo>)</mo><mo>&#x000A0;</mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>X</mi></mrow><mo>&#x000AF;</mo></mover><mo>=</mo><mo>#</mo><mi>h</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#x000A0;</mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>Y</mi></mrow><mo>&#x000AF;</mo></mover><mo>=</mo><mo>#</mo><mi>n</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo>&#x000A0;</mo><msub><mi>&#x003C3;</mi><mrow><mi>X</mi><mi>Y</mi></mrow></msub><mo>=</mo><mo>#</mo><mi>c</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">8</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">25 25 50</data><data name="casSession"/></localData></question> 1.6.3.15Q CovarAmbFreqüències Aquesta taula correspon a les hores passades treballant en el Moodle (Xi) i les notes (Yi) d'un grup d'estudiants de batxillerat. (Fi és la freqüència absoluta de cada parell de dades)
Arrodoneix els resultats trobats amb l'Excel als centèsims.

Xi

Yi

Fi
#x1
 #y1
 #F1
#x2
 #y2
 #F2
#x3
 #y3
 #F3
#x4
 #y4
 #F4
#x5
 #y5
 #F5
#x6
 #y6
 #F6



a ) Calcula la mitjana d'hores passades en el Moodle
És la suma dels Xi·fi (fi és la freqüència relativa de cada parell de dades)
b) Calcula la mitjana de les notes obtingudes
És la suma dels Yi·fi
c) Calcula la covariància amb l'Excel

]]> 1.0000000 0.3333333 0 0 a) =#Xb) =#Yc) =#C]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x4</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x5</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x6</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>y1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y2</mi><mo>=</mo><mi>y1</mi><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>y3</mi><mo>=</mo><mi>y2</mi><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>y4</mi><mo>=</mo><mi>y3</mi><mo>-</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>y5</mi><mo>=</mo><mi>y4</mi></mtd></mtr><mtr><mtd><mi>y6</mi><mo>=</mo><mi>y5</mi><mo>+</mo><mn>1</mn></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>F1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>F2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>F3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>F4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>F5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>F6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>sf</mi><mo>=</mo><mi>F1</mi><mo>+</mo><mi>F2</mi><mo>+</mo><mi>F3</mi><mo>+</mo><mi>F4</mi><mo>+</mo><mi>F5</mi><mo>+</mo><mi>F6</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>sf</mi><mo>,</mo><mn>10</mn><mo>)</mo><mo>≠</mo><mn>1</mn></mrow></mfenced></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X1</mi><mo>=</mo><mi>x1</mi><mo>*</mo><mfrac><mi>F1</mi><mi>sf</mi></mfrac><mo>+</mo><mi>x2</mi><mo>*</mo><mfrac><mi>F2</mi><mi>sf</mi></mfrac><mo>+</mo><mi>x3</mi><mo>*</mo><mfrac><mi>F3</mi><mi>sf</mi></mfrac><mo>+</mo><mi>x4</mi><mo>*</mo><mfrac><mi>F4</mi><mi>sf</mi></mfrac><mo>+</mo><mi>x5</mi><mo>*</mo><mfrac><mi>F5</mi><mi>sf</mi></mfrac><mo>+</mo><mi>x6</mi><mo>*</mo><mfrac><mi>F6</mi><mi>sf</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>X1</mi><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y1</mi><mo>=</mo><mi>y1</mi><mo>*</mo><mfrac><mi>F1</mi><mi>sf</mi></mfrac><mo>+</mo><mi>y2</mi><mo>*</mo><mfrac><mi>F2</mi><mi>sf</mi></mfrac><mo>+</mo><mi>y3</mi><mo>*</mo><mfrac><mi>F3</mi><mi>sf</mi></mfrac><mo>+</mo><mi>y4</mi><mo>*</mo><mfrac><mi>F4</mi><mi>sf</mi></mfrac><mo>+</mo><mi>y5</mi><mo>*</mo><mfrac><mi>F5</mi><mi>sf</mi></mfrac><mo>+</mo><mi>y6</mi><mo>*</mo><mfrac><mi>F6</mi><mi>sf</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>Y1</mi><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mo>(</mo><mi>x1</mi><mo>-</mo><mi>X1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y1</mi><mo>-</mo><mi>Y1</mi><mo>)</mo><mo>*</mo><mfrac><mi>F1</mi><mi>sf</mi></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mo>(</mo><mi>x2</mi><mo>-</mo><mi>X1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y2</mi><mo>-</mo><mi>Y1</mi><mo>)</mo><mo>*</mo><mfrac><mi>F2</mi><mi>sf</mi></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mo>(</mo><mi>x3</mi><mo>-</mo><mi>X1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y3</mi><mo>-</mo><mi>Y1</mi><mo>)</mo><mo>*</mo><mfrac><mi>F3</mi><mi>sf</mi></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c4</mi><mo>=</mo><mo>(</mo><mi>x4</mi><mo>-</mo><mi>X1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y4</mi><mo>-</mo><mi>Y1</mi><mo>)</mo><mo>*</mo><mfrac><mi>F4</mi><mi>sf</mi></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c5</mi><mo>=</mo><mo>(</mo><mi>x5</mi><mo>-</mo><mi>X1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y5</mi><mo>-</mo><mi>Y1</mi><mo>)</mo><mo>*</mo><mfrac><mi>F5</mi><mi>sf</mi></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c6</mi><mo>=</mo><mo>(</mo><mi>x6</mi><mo>-</mo><mi>X1</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y6</mi><mo>-</mo><mi>Y1</mi><mo>)</mo><mo>*</mo><mfrac><mi>F6</mi><mi>sf</mi></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C1</mi><mo>=</mo><mi>c1</mi><mo>+</mo><mi>c2</mi><mo>+</mo><mi>c3</mi><mo>+</mo><mi>c4</mi><mo>+</mo><mi>c5</mi><mo>+</mo><mi>c6</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>C1</mi><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerància</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>X</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>Y</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>C</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">8</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> 1.6.3.20DT Coeficient de Pearson  

Coeficient de correlació de Pearson
Mesura el grau de correlació.
Si és positiu, la correlació és directa; si és negatiu, la correlació és inversa.
Si, en valor absolut, és superior a 0,5, la correlació és forta; en cas contrari, és dèbil.
Es calcula amb:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathcolor=¨#003300¨»§#160;«/mo»«mo mathcolor=¨#003300¨»=«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«mfrac mathcolor=¨#003300¨»«msub»«mi mathvariant=¨bold¨»§#963;«/mi»«mi mathvariant=¨bold¨»XY«/mi»«/msub»«mrow»«msub»«mi mathvariant=¨bold¨»§#963;«/mi»«mi mathvariant=¨bold¨»X«/mi»«/msub»«mo»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»§#963;«/mi»«mi mathvariant=¨bold¨»Y«/mi»«/msub»«/mrow»«/mfrac»«/math»
]]> 0.0000000 0.0000000 0 1.6.3.21Q CàlculCoefCorrelació S'estudia la relació entre la quantitat de llegums ingerits (Xi) i la producció de gas (Yi) en un grup d'individus, amb els resultats següents:

Arrodoneix als centèsims els resultats de l'Excel

Xi

Yi
#x1 #y1
#x2 #y2
#x3 #y3
#x4 #y4
#x5 #y5

 

a) Calcula la mitjana de llegum ingerits

b) Calcula la mitjana de la producció de gas
c) Calcula la covariància «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#963;«/mi»«mi mathvariant=¨bold¨»xy«/mi»«/msub»«/math» 

d) Calcula el coeficient de correlació (Pearson) r



]]> 1.0000000 0.3333333 0 0 a) X¯ =#hb) Y¯ =#nc) σXY=#cd) r =#p]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mn>100</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mn>20</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>=</mo><mi>x2</mi><mo>+</mo><mn>20</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x4</mi><mo>=</mo><mi>x3</mi><mo>+</mo><mn>20</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x5</mi><mo>=</mo><mi>x4</mi><mo>+</mo><mn>20</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>y1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>12</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>12</mn><mo>,</mo><mn>16</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>15</mn><mo>,</mo><mn>20</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>18</mn><mo>,</mo><mn>24</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>28</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mi>x3</mi><mo>,</mo><mi>x4</mi><mo>,</mo><mi>x5</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y1</mi><mo>,</mo><mi>y2</mi><mo>,</mo><mi>y3</mi><mo>,</mo><mi>y4</mi><mo>,</mo><mi>y5</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>mitjana</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>mitjana</mi><mo>(</mo><mi>Y</mi><mo>)</mo><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mfenced><mrow><mo>(</mo><mn>100</mn><mo>*</mo><mo>(</mo><mi>x1</mi><mo>-</mo><mi>h</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y1</mi><mo>-</mo><mi>n</mi><mo>)</mo></mrow></mfenced><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mfenced><mrow><mo>(</mo><mn>100</mn><mo>*</mo><mo>(</mo><mi>x2</mi><mo>-</mo><mi>h</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y2</mi><mo>-</mo><mi>n</mi><mo>)</mo><mo>)</mo></mrow></mfenced></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mfenced><mrow><mo>(</mo><mn>100</mn><mo>*</mo><mo>(</mo><mi>x3</mi><mo>-</mo><mi>h</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y3</mi><mo>-</mo><mi>n</mi><mo>)</mo></mrow></mfenced><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t4</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mfenced><mrow><mo>(</mo><mn>100</mn><mo>*</mo><mo>(</mo><mi>x4</mi><mo>-</mo><mi>h</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y4</mi><mo>-</mo><mi>n</mi><mo>)</mo><mo>)</mo></mrow></mfenced></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t5</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mfenced><mrow><mo>(</mo><mn>100</mn><mo>*</mo><mo>(</mo><mi>x5</mi><mo>-</mo><mi>h</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y5</mi><mo>-</mo><mi>n</mi><mo>)</mo><mo>)</mo></mrow></mfenced></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mfenced><mrow><mi>t1</mi><mo>+</mo><mi>t2</mi><mo>+</mo><mi>t3</mi><mo>+</mo><mi>t4</mi><mo>+</mo><mi>t5</mi></mrow></mfenced><mo>/</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>correlació</mi><mo>(</mo><mi>X</mi><mo>,</mo><mi>Y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>p1</mi><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerància</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:wrs="http://www.wiris.com/xml/mathml-extension"><mi>a</mi><mo>)</mo><mo>&#x02009;</mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>X</mi></mrow><mo>&#x000AF;</mo></mover><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>h</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#x000A0;</mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>Y</mi></mrow><mo>&#x000AF;</mo></mover><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>n</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo>&#x000A0;</mo><msub><mi>&#x003C3;</mi><mrow><mi>X</mi><mi>Y</mi></mrow></msub><mo>=</mo><mo>#</mo><mi>c</mi><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mo>)</mo><mo>&#x000A0;</mo><mi>r</mi><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>p</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">25 25 25 25</data><data name="inputField">popupEditor</data><data name="casSession"/></localData></question> 1.6.3.25Q InterpretaCoefCorrel S'estudia la relació entre les variables Xi i Yi a partir dels resultats següents:

Xi

Yi
#x1 #y1
#x2 #y2
#x3 #y3
#x4 #y4
#x5 #y5

Fes servir l'Excel per fer els càlculs (arrodoneix als centèsims)

a).Calcula la mitjana de Xi

b) Calcula la mitjana de Yi

c) Calcula la covariància «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub mathcolor=¨#7F007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#7F007F¨»§#963;«/mi»«mi mathvariant=¨bold¨»xy«/mi»«/msub»«/math»

d) Calcula  el coeficient de correlació (Pearson) r
e) Classifica la correlació {D,d}. D per directa, I per inversa, F per forta i  d per dèbil. Directa si és positiva, indirecta si és negativa. Forta si, en valor absolut,  és més gran que 0.5, feble en cas contrari.

]]> 1.0000000 0.3333333 0 0 a) X¯=#hb) Y¯=#nc) σxy=#cd) r = #pe) Tipus =#sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mn>10</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>=</mo><mi>x2</mi><mo>+</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x4</mi><mo>=</mo><mi>x3</mi><mo>+</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x5</mi><mo>=</mo><mi>x4</mi><mo>+</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>50</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>60</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>40</mn><mo>,</mo><mn>70</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>40</mn><mo>,</mo><mn>80</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>90</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>a_1</mi><mo>,</mo><mi>a_5</mi></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>y1</mi><mo>=</mo><mi>a_1</mi></mrow><mtable><mtr><mtd><mi>y2</mi><mo>=</mo><mi>a_2</mi></mtd></mtr><mtr><mtd><mi>y3</mi><mo>=</mo><mi>a_3</mi></mtd></mtr><mtr><mtd><mi>y4</mi><mo>=</mo><mi>a_4</mi></mtd></mtr><mtr><mtd><mi>y5</mi><mo>=</mo><mi>a_5</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>y2</mi><mo>=</mo><mi>a_4</mi></mtd></mtr><mtr><mtd><mi>y3</mi><mo>=</mo><mi>a_3</mi></mtd></mtr><mtr><mtd><mi>y4</mi><mo>=</mo><mi>a_2</mi></mtd></mtr><mtr><mtd><mi>y5</mi><mo>=</mo><mi>a_1</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mi>x3</mi><mo>,</mo><mi>x4</mi><mo>,</mo><mi>x5</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y1</mi><mo>,</mo><mi>y2</mi><mo>,</mo><mi>y3</mi><mo>,</mo><mi>y4</mi><mo>,</mo><mi>y5</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>mitjana</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>mitjana</mi><mo>(</mo><mi>Y</mi><mo>)</mo><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math 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open="|"><mi>p</mi></mfenced><mo>&gt;</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow><mtable><mtr><mtd><mi>j_1</mi><mo>=</mo><mi>F</mi></mtd></mtr><mtr><mtd><mi>j_2</mi><mo>=</mo><mi>d</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>j_2</mi><mo>=</mo><mi>F</mi></mtd></mtr><mtr><mtd><mi>j_1</mi><mo>=</mo><mi>d</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>i_1</mi><mo>,</mo><mi>j_1</mi></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>,</mo><mi>Y</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable 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xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>I</mi><mo>,</mo><mi>d</mi></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:wrs="http://www.wiris.com/xml/mathml-extension"><mi>a</mi><mo>)</mo><mo>&#x000A0;</mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>X</mi></mrow><mo>&#x000AF;</mo></mover><mo>=</mo><mo>#</mo><mi>h</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#x000A0;</mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>Y</mi></mrow><mo>&#x000AF;</mo></mover><mo>=</mo><mo>#</mo><mi>n</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo>&#x000A0;</mo><msub><mi>&#x003C3;</mi><mrow><mi>x</mi><mi>y</mi></mrow></msub><mo>=</mo><mo>#</mo><mi>c</mi><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mo>)</mo><mo>&#x000A0;</mo><mi>r</mi><mo>&#x000A0;</mo><mo>=</mo><mo>&#x000A0;</mo><mo>#</mo><mi>p</mi><mspace linebreak="newline"/><mi mathvariant="normal">e</mi><mo>)</mo><mo>&#x000A0;</mo><mi>T</mi><mi mathvariant="normal">i</mi><mi>p</mi><mi>u</mi><mi>s</mi><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">8</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">10 10 20 30 30</data><data name="casSession"/></localData></question> 1.6.3.26Q InterpretaCoefCorrel_2 S'estudia la relació entre les variables Xi i Yi a partir dels resultats següents:

 

Xi

Yi
#x1 #y1
#x2 #y2
#x3 #y3
#x4 #y4
#x5 #y5

Fes servir l'Excel per fer els càlculs (arrodoneix als centèsims)
a).Calcula la mitjana de Xi
b) Calcula la mitjana de Yi
c) Calcula la covariància «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub mathcolor=¨#7F007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#7F007F¨»§#963;«/mi»«mi mathvariant=¨bold¨»xy«/mi»«/msub»«/math»

d) Calcula  el coeficient de correlació (Pearson) r
e) Classifica la correlació {D,d}. D per directa, I per inversa, F per forta i  d per dèbil. Directa si és positiva, indirecta si és negativa. Forta si, en valor absolut,  és més gran que 0.5, feble en cas contrari.

]]> 1.0000000 0.3333333 0 0 a) X¯=#hb) Y¯=#nc) σxy=#cd) r = #pe) Tipus =#sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mn>100</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>10</mn><mo>,</mo><mn>20</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>=</mo><mi>x2</mi><mo>+</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>10</mn><mo>,</mo><mn>20</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x4</mi><mo>=</mo><mi>x3</mi><mo>+</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>10</mn><mo>,</mo><mn>20</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x5</mi><mo>=</mo><mi>x4</mi><mo>+</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>10</mn><mo>,</mo><mn>20</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mfenced><mrow><mo>(</mo><mn>100</mn><mo>*</mo><mo>(</mo><mi>x3</mi><mo>-</mo><mi>h</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y3</mi><mo>-</mo><mi>n</mi><mo>)</mo></mrow></mfenced><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t4</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mfenced><mrow><mo>(</mo><mn>100</mn><mo>*</mo><mo>(</mo><mi>x4</mi><mo>-</mo><mi>h</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y4</mi><mo>-</mo><mi>n</mi><mo>)</mo><mo>)</mo></mrow></mfenced></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t5</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mfenced><mrow><mo>(</mo><mn>100</mn><mo>*</mo><mo>(</mo><mi>x5</mi><mo>-</mo><mi>h</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y5</mi><mo>-</mo><mi>n</mi><mo>)</mo><mo>)</mo></mrow></mfenced></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mfrac><mfenced><mrow><mi>t1</mi><mo>+</mo><mi>t2</mi><mo>+</mo><mi>t3</mi><mo>+</mo><mi>t4</mi><mo>+</mo><mi>t5</mi></mrow></mfenced><mn>5</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_1</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>desviació_estàndard_n</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mi>x3</mi><mo>,</mo><mi>x4</mi><mo>,</mo><mi>x5</mi></mtd></mtr></mtable></mfenced><mo>)</mo><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_2</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>desviació_estàndard_n</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y1</mi><mo>,</mo><mi>y2</mi><mo>,</mo><mi>y3</mi><mo>,</mo><mi>y4</mi><mo>,</mo><mi>y5</mi></mtd></mtr></mtable></mfenced><mo>)</mo><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mfrac><mi>c</mi><mrow><mi>d_1</mi><mo>*</mo><mi>d_2</mi></mrow></mfrac><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>p</mi><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>i_1</mi><mo>=</mo><mi>D</mi></mtd></mtr><mtr><mtd><mi>i_2</mi><mo>=</mo><mi>I</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>i_1</mi><mo>=</mo><mi>I</mi></mtd></mtr><mtr><mtd><mi>i_2</mi><mo>=</mo><mi>D</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mfenced close="|" open="|"><mi>p</mi></mfenced><mo>&gt;</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow><mtable><mtr><mtd><mi>j_1</mi><mo>=</mo><mi>F</mi></mtd></mtr><mtr><mtd><mi>j_2</mi><mo>=</mo><mi>d</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>j_2</mi><mo>=</mo><mi>F</mi></mtd></mtr><mtr><mtd><mi>j_1</mi><mo>=</mo><mi>d</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>i_1</mi><mo>,</mo><mi>j_1</mi></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>,</mo><mi>Y</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable 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xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>I</mi><mo>,</mo><mi>d</mi></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:wrs="http://www.wiris.com/xml/mathml-extension"><mi>a</mi><mo>)</mo><mo>&#x000A0;</mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>X</mi></mrow><mo>&#x000AF;</mo></mover><mo>=</mo><mo>#</mo><mi>h</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#x000A0;</mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>Y</mi></mrow><mo>&#x000AF;</mo></mover><mo>=</mo><mo>#</mo><mi>n</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo>&#x000A0;</mo><msub><mi>&#x003C3;</mi><mrow><mi>x</mi><mi>y</mi></mrow></msub><mo>=</mo><mo>#</mo><mi>c</mi><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mo>)</mo><mo>&#x000A0;</mo><mi>r</mi><mo>&#x000A0;</mo><mo>=</mo><mo>&#x000A0;</mo><mo>#</mo><mi>p</mi><mspace linebreak="newline"/><mi mathvariant="normal">e</mi><mo>)</mo><mo>&#x000A0;</mo><mi>T</mi><mi mathvariant="normal">i</mi><mi>p</mi><mi>u</mi><mi>s</mi><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">8</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">10 10 20 30 30</data><data name="casSession"/></localData></question> 1.6.3.30DT Recta de regressió  

Recta de regressió
Si la correlació és lineal i forta, es pot ajustar la distribució a una recta, que permet fer prediccions, i que s'anomena recta de regressió.
Es calcula amb:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»y«/mi»«mo mathcolor=¨#003300¨»§#160;«/mo»«mo mathcolor=¨#003300¨»-«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«mover mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»Y«/mi»«mo»§#175;«/mo»«/mover»«mo mathcolor=¨#003300¨»=«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«mfrac mathcolor=¨#003300¨»«msub»«mi mathvariant=¨bold¨»§#963;«/mi»«mi mathvariant=¨bold¨»XY«/mi»«/msub»«mrow»«msub»«mi mathvariant=¨bold¨»§#963;«/mi»«mi mathvariant=¨bold¨»X«/mi»«/msub»«mo»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»§#963;«/mi»«mi mathvariant=¨bold¨»Y«/mi»«/msub»«/mrow»«/mfrac»«mfenced mathcolor=¨#003300¨»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo»§#160;«/mo»«mo»-«/mo»«mo»§#160;«/mo»«mover»«mi mathvariant=¨bold¨»X«/mi»«mo»§#175;«/mo»«/mover»«/mrow»«/mfenced»«/math»
Si és la de Y sobre X
]]> 0.0000000 0.0000000 0 1.6.3.31Q RectaRegRaspallat S'estudia la relació entre freqüència de raspallat de dents (Xi) i l'aparició de càries (Yi) en un grup d'individus, amb els resultats següents:

Xi

Yi
#x1 #y1
#x2 #y2
#x3 #y3
#x4 #y4
#x5 #y5

Arrodoneix als centèsims.
a) Calcula la mitjana de raspallats al dia «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»X«/mi»«mo mathvariant=¨bold¨»§#175;«/mo»«/mover»«/math»

b) Calcula la mitjana d'aparició de càries  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»Y«/mi»«mo mathvariant=¨bold¨»§#175;«/mo»«/mover»«/math»

c) Calcula la covariància «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#963;«/mi»«mi mathvariant=¨bold¨»XY«/mi»«/msub»«/math»

d) Calcula  el coeficient de correlació (Pearson) r

e) Determina  l'equació y = mx+n de la recta de regressió?

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#G

]]> 1.0000000 0.3333333 0 0 a) X¯ =#Xb) Y¯= #Yc) σXY=#cd) r =#pe) equació =#e]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>y1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>mitjana</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mi>x3</mi><mo>,</mo><mi>x4</mi><mo>,</mo><mi>x5</mi></mtd></mtr></mtable></mfenced><mo>)</mo><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>mitjana</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y1</mi><mo>,</mo><mi>y2</mi><mo>,</mo><mi>y3</mi><mo>,</mo><mi>y4</mi><mo>,</mo><mi>y5</mi></mtd></mtr></mtable></mfenced><mo>)</mo><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mo>(</mo><mi>x1</mi><mo>-</mo><mi>X</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y1</mi><mo>-</mo><mi>Y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mo>(</mo><mi>x2</mi><mo>-</mo><mi>X</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y2</mi><mo>-</mo><mi>Y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mo>(</mo><mi>x3</mi><mo>-</mo><mi>X</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y3</mi><mo>-</mo><mi>Y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t4</mi><mo>=</mo><mo>(</mo><mi>x4</mi><mo>-</mo><mi>X</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y4</mi><mo>-</mo><mi>Y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t5</mi><mo>=</mo><mo>(</mo><mi>x5</mi><mo>-</mo><mi>X</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y5</mi><mo>-</mo><mi>Y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mfenced><mrow><mi>t1</mi><mo>+</mo><mi>t2</mi><mo>+</mo><mi>t3</mi><mo>+</mo><mi>t4</mi><mo>+</mo><mi>t5</mi></mrow></mfenced><mo>/</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>desviació_estàndard_n</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mi>x3</mi><mo>,</mo><mi>x4</mi><mo>,</mo><mi>x5</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>desviació_estàndard_n</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y1</mi><mo>,</mo><mi>y2</mi><mo>,</mo><mi>y3</mi><mo>,</mo><mi>y4</mi><mo>,</mo><mi>y5</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mfrac><mi>c</mi><mrow><mi>d1</mi><mo>*</mo><mi>d2</mi></mrow></mfrac><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mfrac><mi>c</mi><msup><mfenced><mi>d1</mi></mfenced><mn>2</mn></msup></mfrac><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mfrac><mi>c</mi><msup><mfenced><mi>d1</mi></mfenced><mn>2</mn></msup></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>X</mi><mo>)</mo><mo>+</mo><mi>Y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>punt</mi><mo>(</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>)</mo><mo>,</mo><mi>punt</mi><mo>(</mo><mi>x2</mi><mo>,</mo><mi>y2</mi><mo>)</mo><mo>,</mo><mi>punt</mi><mo>(</mo><mi>x3</mi><mo>,</mo><mi>y3</mi><mo>)</mo><mo>,</mo><mi>punt</mi><mo>(</mo><mi>x4</mi><mo>,</mo><mi>y4</mi><mo>)</mo><mo>,</mo><mi>punt</mi><mo>(</mo><mi>x5</mi><mo>,</mo><mi>y5</mi><mo>)</mo></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>recta_de_regressió</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada</mi><mo>=</mo><mn>210</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>265</mn><mo>,</mo><mi>centre</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mn>105</mn><mo>,</mo><mn>55</mn><mo>)</mo></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>T</mi><mo>,</mo><mi>L</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>mida_punt</mi><mo>=</mo><mn>5</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>T</mi><mo>,</mo><mi>r</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>correlació</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerància</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mi>x3</mi><mo>,</mo><mi>x4</mi><mo>,</mo><mi>x5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>160</mn><mo>,</mo><mn>162</mn><mo>,</mo><mn>167</mn><mo>,</mo><mn>173</mn><mo>,</mo><mn>180</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>,</mo><mi>y2</mi><mo>,</mo><mi>y3</mi><mo>,</mo><mi>y4</mi><mo>,</mo><mi>y5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>155</mn><mo>,</mo><mn>161</mn><mo>,</mo><mn>168</mn><mo>,</mo><mn>174</mn><mo>,</mo><mn>179</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>,</mo><mi>Y</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>168.4</mn><mo>,</mo><mn>167.4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>,</mo><mi>t2</mi><mo>,</mo><mi>t3</mi><mo>,</mo><mi>t4</mi><mo>,</mo><mi>t5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>104.16</mn><mo>,</mo><mn>40.96</mn><mo>,</mo><mo>-</mo><mn>0.84</mn><mo>,</mo><mn>30.36</mn><mo>,</mo><mn>134.56</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>,</mo><mi>d2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7.3376</mn><mo>,</mo><mn>8.6394</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>61.84</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.98</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>1.1486</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>26.022</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>1.1486</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>26.022</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:wrs="http://www.wiris.com/xml/mathml-extension"><mi>a</mi><mo>)</mo><mo>&#x000A0;</mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>X</mi></mrow><mo>&#x000AF;</mo></mover><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>X</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#x000A0;</mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>Y</mi></mrow><mo>&#x000AF;</mo></mover><mo>=</mo><mo>&#x000A0;</mo><mo>#</mo><mi>Y</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo>&#x000A0;</mo><msub><mi>&#x003C3;</mi><mrow><mi>X</mi><mi>Y</mi></mrow></msub><mo>=</mo><mo>#</mo><mi>c</mi><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mo>)</mo><mo>&#x000A0;</mo><mi>r</mi><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>p</mi><mspace linebreak="newline"/><mi mathvariant="normal">e</mi><mo>)</mo><mo>&#x000A0;</mo><mi mathvariant="normal">e</mi><mi>q</mi><mi>u</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>&#x000F3;</mi><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">e</mi><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">8</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">10 10 20 20 40</data><data name="inputField">popupEditor</data><data name="casSession"/></localData></question> 1.6.3.32Q RectaRegParesFills S'estudia la relació entre la talla dels pares (Xi) i la talla dels fills (Yi) en un grup d'individus, amb els resultats següents:

Xi

Yi
#x1 #y1
#x2 #y2
#x3 #y3
#x4 #y4
#x5 #y5

Arrodoneix als centèsims.
a) Calcula la mitjana d'altura dels pares «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»X«/mi»«mo mathvariant=¨bold¨»§#175;«/mo»«/mover»«/math»

b) Calcula la mitjana d'altura dels fills «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»Y«/mi»«mo mathvariant=¨bold¨»§#175;«/mo»«/mover»«/math»

c) Calcula la covariància «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#963;«/mi»«mi mathvariant=¨bold¨»XY«/mi»«/msub»«/math»

d) Calcula  el coeficient de correlació (Pearson) r

e) Determina  l'equació y = mx+n de la recta de regressió?

]]> Els punts i la recta de regressió es poden representar així:
#G

]]> 1.0000000 0.3333333 0 0 a) X¯ =#Xb) Y¯= #Yc) σXY=#cd) r =#pe) equació =#e]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>150</mn><mo>,</mo><mn>160</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>=</mo><mi>x2</mi><mo>+</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x4</mi><mo>=</mo><mi>x3</mi><mo>+</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x5</mi><mo>=</mo><mi>x4</mi><mo>+</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>155</mn><mo>,</mo><mn>170</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y2</mi><mo>=</mo><mi>y1</mi><mo>+</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y3</mi><mo>=</mo><mi>y2</mi><mo>+</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y4</mi><mo>=</mo><mi>y3</mi><mo>+</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y5</mi><mo>=</mo><mi>y4</mi><mo>+</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>mitjana</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mi>x3</mi><mo>,</mo><mi>x4</mi><mo>,</mo><mi>x5</mi></mtd></mtr></mtable></mfenced><mo>)</mo><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>mitjana</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y1</mi><mo>,</mo><mi>y2</mi><mo>,</mo><mi>y3</mi><mo>,</mo><mi>y4</mi><mo>,</mo><mi>y5</mi></mtd></mtr></mtable></mfenced><mo>)</mo><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mo>(</mo><mi>x1</mi><mo>-</mo><mi>X</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y1</mi><mo>-</mo><mi>Y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mo>(</mo><mi>x2</mi><mo>-</mo><mi>X</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y2</mi><mo>-</mo><mi>Y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mo>(</mo><mi>x3</mi><mo>-</mo><mi>X</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y3</mi><mo>-</mo><mi>Y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t4</mi><mo>=</mo><mo>(</mo><mi>x4</mi><mo>-</mo><mi>X</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y4</mi><mo>-</mo><mi>Y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t5</mi><mo>=</mo><mo>(</mo><mi>x5</mi><mo>-</mo><mi>X</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y5</mi><mo>-</mo><mi>Y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mfenced><mrow><mi>t1</mi><mo>+</mo><mi>t2</mi><mo>+</mo><mi>t3</mi><mo>+</mo><mi>t4</mi><mo>+</mo><mi>t5</mi></mrow></mfenced><mo>/</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>desviació_estàndard_n</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mi>x3</mi><mo>,</mo><mi>x4</mi><mo>,</mo><mi>x5</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>desviació_estàndard_n</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y1</mi><mo>,</mo><mi>y2</mi><mo>,</mo><mi>y3</mi><mo>,</mo><mi>y4</mi><mo>,</mo><mi>y5</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mfrac><mi>c</mi><mrow><mi>d1</mi><mo>*</mo><mi>d2</mi></mrow></mfrac><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mfrac><mi>c</mi><msup><mfenced><mi>d1</mi></mfenced><mn>2</mn></msup></mfrac><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mfrac><mi>c</mi><msup><mfenced><mi>d1</mi></mfenced><mn>2</mn></msup></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>X</mi><mo>)</mo><mo>+</mo><mi>Y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>punt</mi><mo>(</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>)</mo><mo>,</mo><mi>punt</mi><mo>(</mo><mi>x2</mi><mo>,</mo><mi>y2</mi><mo>)</mo><mo>,</mo><mi>punt</mi><mo>(</mo><mi>x3</mi><mo>,</mo><mi>y3</mi><mo>)</mo><mo>,</mo><mi>punt</mi><mo>(</mo><mi>x4</mi><mo>,</mo><mi>y4</mi><mo>)</mo><mo>,</mo><mi>punt</mi><mo>(</mo><mi>x5</mi><mo>,</mo><mi>y5</mi><mo>)</mo></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>recta_de_regressió</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada</mi><mo>=</mo><mn>210</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>265</mn><mo>,</mo><mi>centre</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mn>105</mn><mo>,</mo><mn>55</mn><mo>)</mo></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>T</mi><mo>,</mo><mi>L</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>mida_punt</mi><mo>=</mo><mn>5</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>T</mi><mo>,</mo><mi>r</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>correlació</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerància</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mi>x3</mi><mo>,</mo><mi>x4</mi><mo>,</mo><mi>x5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>160</mn><mo>,</mo><mn>162</mn><mo>,</mo><mn>167</mn><mo>,</mo><mn>173</mn><mo>,</mo><mn>180</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>,</mo><mi>y2</mi><mo>,</mo><mi>y3</mi><mo>,</mo><mi>y4</mi><mo>,</mo><mi>y5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>155</mn><mo>,</mo><mn>161</mn><mo>,</mo><mn>168</mn><mo>,</mo><mn>174</mn><mo>,</mo><mn>179</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>,</mo><mi>Y</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>168.4</mn><mo>,</mo><mn>167.4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>,</mo><mi>t2</mi><mo>,</mo><mi>t3</mi><mo>,</mo><mi>t4</mi><mo>,</mo><mi>t5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>104.16</mn><mo>,</mo><mn>40.96</mn><mo>,</mo><mo>-</mo><mn>0.84</mn><mo>,</mo><mn>30.36</mn><mo>,</mo><mn>134.56</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>,</mo><mi>d2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7.3376</mn><mo>,</mo><mn>8.6394</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>61.84</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.98</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>1.1486</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>26.022</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>1.1486</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>26.022</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:wrs="http://www.wiris.com/xml/mathml-extension"><mi>a</mi><mo>)</mo><mo>&#x000A0;</mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>X</mi></mrow><mo>&#x000AF;</mo></mover><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>X</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#x000A0;</mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>Y</mi></mrow><mo>&#x000AF;</mo></mover><mo>=</mo><mo>&#x000A0;</mo><mo>#</mo><mi>Y</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo>&#x000A0;</mo><msub><mi>&#x003C3;</mi><mrow><mi>X</mi><mi>Y</mi></mrow></msub><mo>=</mo><mo>#</mo><mi>c</mi><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mo>)</mo><mo>&#x000A0;</mo><mi>r</mi><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>p</mi><mspace linebreak="newline"/><mi mathvariant="normal">e</mi><mo>)</mo><mo>&#x000A0;</mo><mi mathvariant="normal">e</mi><mi>q</mi><mi>u</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>&#x000F3;</mi><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">e</mi><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">8</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">10 10 20 20 40</data><data name="inputField">popupEditor</data><data name="casSession"/></localData></question> 1.6.3.33Q RectaRegFertilitzant Per tal d'estudiar l'efecte d'un fertilitzant, es compara la quantitat d'adob (Xi) amb la producció  (Yi) en cinc camps similars, amb els resultats següents:

Xi

Yi
#x1 #y1
#x2 #y2
#x3 #y3
#x4 #y4
#x5 #y5

Arrodoneix als centèsims.
a) Calcula la mitjana de kg de fertilitzant  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#7F007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»X«/mi»«mo mathvariant=¨bold¨»§#175;«/mo»«/mover»«/math»

b) Calcula la mitjana de producció en tonelades «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»Y«/mi»«mo mathvariant=¨bold¨»§#175;«/mo»«/mover»«/math»

c) Calcula la covariància «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#963;«/mi»«mi mathvariant=¨bold¨»XY«/mi»«/msub»«/math»

d) Calcula  el coeficient de correlació (Pearson) r

e) Determina  l'equació y = mx+n de la recta de regressió?

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#G

]]> 1.0000000 0.3333333 0 0 a) X¯ =#Xb) Y¯= #Yc) σXY=#cd) r =#pe) equació =#e]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>y1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>40</mn><mo>,</mo><mn>50</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>40</mn><mo>,</mo><mn>50</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>60</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>60</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>y5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>70</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>mitjana</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mi>x3</mi><mo>,</mo><mi>x4</mi><mo>,</mo><mi>x5</mi></mtd></mtr></mtable></mfenced><mo>)</mo><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>mitjana</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y1</mi><mo>,</mo><mi>y2</mi><mo>,</mo><mi>y3</mi><mo>,</mo><mi>y4</mi><mo>,</mo><mi>y5</mi></mtd></mtr></mtable></mfenced><mo>)</mo><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mo>(</mo><mi>x1</mi><mo>-</mo><mi>X</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y1</mi><mo>-</mo><mi>Y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mo>(</mo><mi>x2</mi><mo>-</mo><mi>X</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y2</mi><mo>-</mo><mi>Y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mo>(</mo><mi>x3</mi><mo>-</mo><mi>X</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y3</mi><mo>-</mo><mi>Y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t4</mi><mo>=</mo><mo>(</mo><mi>x4</mi><mo>-</mo><mi>X</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y4</mi><mo>-</mo><mi>Y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t5</mi><mo>=</mo><mo>(</mo><mi>x5</mi><mo>-</mo><mi>X</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>y5</mi><mo>-</mo><mi>Y</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mfenced><mrow><mi>t1</mi><mo>+</mo><mi>t2</mi><mo>+</mo><mi>t3</mi><mo>+</mo><mi>t4</mi><mo>+</mo><mi>t5</mi></mrow></mfenced><mo>/</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>desviació_estàndard_n</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mi>x3</mi><mo>,</mo><mi>x4</mi><mo>,</mo><mi>x5</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>desviació_estàndard_n</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y1</mi><mo>,</mo><mi>y2</mi><mo>,</mo><mi>y3</mi><mo>,</mo><mi>y4</mi><mo>,</mo><mi>y5</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mfrac><mi>c</mi><mrow><mi>d1</mi><mo>*</mo><mi>d2</mi></mrow></mfrac><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mfrac><mi>c</mi><msup><mfenced><mi>d1</mi></mfenced><mn>2</mn></msup></mfrac><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mfrac><mi>c</mi><msup><mfenced><mi>d1</mi></mfenced><mn>2</mn></msup></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>X</mi><mo>)</mo><mo>+</mo><mi>Y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>punt</mi><mo>(</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>)</mo><mo>,</mo><mi>punt</mi><mo>(</mo><mi>x2</mi><mo>,</mo><mi>y2</mi><mo>)</mo><mo>,</mo><mi>punt</mi><mo>(</mo><mi>x3</mi><mo>,</mo><mi>y3</mi><mo>)</mo><mo>,</mo><mi>punt</mi><mo>(</mo><mi>x4</mi><mo>,</mo><mi>y4</mi><mo>)</mo><mo>,</mo><mi>punt</mi><mo>(</mo><mi>x5</mi><mo>,</mo><mi>y5</mi><mo>)</mo></mtd></mtr></mtable></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>recta_de_regressió</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada</mi><mo>=</mo><mn>210</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>265</mn><mo>,</mo><mi>centre</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mn>105</mn><mo>,</mo><mn>55</mn><mo>)</mo></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>T</mi><mo>,</mo><mi>L</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>mida_punt</mi><mo>=</mo><mn>5</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>T</mi><mo>,</mo><mi>r</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>correlació</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerància</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mi>x3</mi><mo>,</mo><mi>x4</mi><mo>,</mo><mi>x5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>160</mn><mo>,</mo><mn>162</mn><mo>,</mo><mn>167</mn><mo>,</mo><mn>173</mn><mo>,</mo><mn>180</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>,</mo><mi>y2</mi><mo>,</mo><mi>y3</mi><mo>,</mo><mi>y4</mi><mo>,</mo><mi>y5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>155</mn><mo>,</mo><mn>161</mn><mo>,</mo><mn>168</mn><mo>,</mo><mn>174</mn><mo>,</mo><mn>179</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>,</mo><mi>Y</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>168.4</mn><mo>,</mo><mn>167.4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>,</mo><mi>t2</mi><mo>,</mo><mi>t3</mi><mo>,</mo><mi>t4</mi><mo>,</mo><mi>t5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>104.16</mn><mo>,</mo><mn>40.96</mn><mo>,</mo><mo>-</mo><mn>0.84</mn><mo>,</mo><mn>30.36</mn><mo>,</mo><mn>134.56</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>,</mo><mi>d2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7.3376</mn><mo>,</mo><mn>8.6394</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>61.84</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.98</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>1.1486</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>26.022</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>1.1486</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>26.022</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:wrs="http://www.wiris.com/xml/mathml-extension"><mi>a</mi><mo>)</mo><mo>&#x000A0;</mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>X</mi></mrow><mo>&#x000AF;</mo></mover><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>X</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#x000A0;</mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>Y</mi></mrow><mo>&#x000AF;</mo></mover><mo>=</mo><mo>&#x000A0;</mo><mo>#</mo><mi>Y</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo>&#x000A0;</mo><msub><mi>&#x003C3;</mi><mrow><mi>X</mi><mi>Y</mi></mrow></msub><mo>=</mo><mo>#</mo><mi>c</mi><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mo>)</mo><mo>&#x000A0;</mo><mi>r</mi><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>p</mi><mspace linebreak="newline"/><mi mathvariant="normal">e</mi><mo>)</mo><mo>&#x000A0;</mo><mi mathvariant="normal">e</mi><mi>q</mi><mi>u</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>&#x000F3;</mi><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">e</mi><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">8</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">10 10 20 20 40</data><data name="inputField">popupEditor</data><data name="casSession"/></localData></question> 1.6.3.35Q ExtrapRegParesFills S'estudia la relació entre la talla dels pares (Xi) i la talla dels fills (Yi) en un grup d'individus, amb els resultats següents:

Xi

Yi
#x1 #y1
#x2 #y2
#x3 #y3
#x4 #y4
#x5 #y5

Arrodoneix als centèsims.

a) Calcula  el coeficient de correlació (Pearson) r

b) Determina  l'equació y = mx+n de la recta de regressió?

c) Quina alçada (en cm) cal esperar pel fill d'un pare de #k1 cm?

 

]]> Els punts i la recta de regressió es poden representar així:
#G

]]> 1.0000000 0.3333333 0 0 a) r =#pb) equació =#ec) Alçada =#k2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>x1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>150</mn><mo>,</mo><mn>160</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>x2</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>x3</mi><mo>=</mo><mi>x2</mi><mo>+</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>x4</mi><mo>=</mo><mi>x3</mi><mo>+</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>x5</mi><mo>=</mo><mi>x4</mi><mo>+</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>7</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>150</mn><mo>,</mo><mn>185</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>k1</mi><mo>∉</mo><mfenced close="}" open="{"><mtable 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>y4</mi><mo>=</mo><mi>y3</mi><mo>+</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y5</mi><mo>=</mo><mi>y4</mi><mo>+</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>mitjana</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mi>x3</mi><mo>,</mo><mi>x4</mi><mo>,</mo><mi>x5</mi></mtd></mtr></mtable></mfenced><mo>)</mo><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>T</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mi>k1</mi><mo>,</mo><mi>k2</mi><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>mida_punt</mi><mo>=</mo><mn>7</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>verd</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tolerància</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>,</mo><mi>x2</mi><mo>,</mo><mi>x3</mi><mo>,</mo><mi>x4</mi><mo>,</mo><mi>x5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>160</mn><mo>,</mo><mn>164</mn><mo>,</mo><mn>170</mn><mo>,</mo><mn>175</mn><mo>,</mo><mn>180</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>,</mo><mi>y2</mi><mo>,</mo><mi>y3</mi><mo>,</mo><mi>y4</mi><mo>,</mo><mi>y5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>167</mn><mo>,</mo><mn>173</mn><mo>,</mo><mn>181</mn><mo>,</mo><mn>186</mn><mo>,</mo><mn>191</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>,</mo><mi>Y</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>169.8</mn><mo>,</mo><mn>179.6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>,</mo><mi>t2</mi><mo>,</mo><mi>t3</mi><mo>,</mo><mi>t4</mi><mo>,</mo><mi>t5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>123.48</mn><mo>,</mo><mn>38.28</mn><mo>,</mo><mn>0.28</mn><mo>,</mo><mn>33.28</mn><mo>,</mo><mn>116.28</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>,</mo><mi>d2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7.2222</mn><mo>,</mo><mn>8.6626</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>62.32</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>1.1948</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>23.275</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>1.1948</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>23.275</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>,</mo><mi>k2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>181</mn><mo>,</mo><mn>192.98</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo>&#x000A0;</mo><mi>r</mi><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>p</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>&#x000A0;</mo><mi mathvariant="normal">e</mi><mi>q</mi><mi>u</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>&#x000F3;</mi><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">e</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo>&#x000A0;</mo><mi>A</mi><mi>l</mi><mi>&#x000E7;</mi><mi>a</mi><mi mathvariant="normal">d</mi><mi>a</mi><mo>&#x000A0;</mo><mo>=</mo><mo>#</mo><mi>k</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">8</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">30 30 40</data><data name="inputField">popupEditor</data><data name="casSession"/></localData></question> 1.6.3.37Q PrediccióMòbils Entre els anys (Xi) #x1 i #x5 es van vendre Yi  mòbils en els anys successius amb els resultats següents:

Xi

  

Yi
#X Mitjana #Y
#d1 Desviació típica #d2

el coeficient de correlació va ser #r

a) Escriu l'equació de la recta de regressió y = mx + n

b) Quants mòbils es preveu que es vendran l'any #A?

Arrodoneix els resultats  als centèsims.

 

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