1rBTX 06. ESTADÍSTICA/1.6.3 Bidimensional 1.6.3.10DT Covariància

Covariància

La covariància és la mitjana dels productes de les desviacions de X_i i de Y_i 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:

X_i	Y_i
#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 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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> </mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>X</mi></mrow><mo>¯</mo></mover><mo>=</mo><mo>#</mo><mi>h</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>Y</mi></mrow><mo>¯</mo></mover><mo>=</mo><mo>#</mo><mi>n</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo> </mo><msub><mi>σ</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 (X_i) i les notes (Y_i) d'un grup d'estudiants de batxillerat. (F_i és la freqüència absoluta de cada parell de dades)
Arrodoneix els resultats trobats amb l'Excel als centèsims.

X_i	Y_i	F_i
#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 X_i·f_i (f_i és la freqüència relativa de cada parell de dades)
b) Calcula la mitjana de les notes obtingudes
És la suma dels Y_i·f_i
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 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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 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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> </mo><mo>=</mo><mo>#</mo><mi>X</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>Y</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo> </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 (X_i) i la producció de gas (Y_i) en un grup d'individus, amb els resultats següents:

Arrodoneix als centèsims els resultats de l'Excel

X_i	Y_i
#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> </mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>X</mi></mrow><mo>¯</mo></mover><mo> </mo><mo>=</mo><mo>#</mo><mi>h</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>Y</mi></mrow><mo>¯</mo></mover><mo> </mo><mo>=</mo><mo>#</mo><mi>n</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo> </mo><msub><mi>σ</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> </mo><mi>r</mi><mo> </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 X_i i Y_i a partir dels resultats següents:

X_i	Y_i
#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 X_i

b) Calcula la mitjana de Y_i

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 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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>></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>></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 align="center"><mtr><mtd><mn>500</mn><mo>,</mo><mn>520</mn><mo>,</mo><mn>540</mn><mo>,</mo><mn>560</mn><mo>,</mo><mn>580</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>46</mn><mo>,</mo><mn>61</mn><mo>,</mo><mn>35</mn><mo>,</mo><mn>33</mn><mo>,</mo><mn>48</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>540.</mn><mo>,</mo><mn>44.6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>,</mo><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>96.</mn><mo>,</mo><mo>-</mo><mn>0.34</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><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> </mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>X</mi></mrow><mo>¯</mo></mover><mo>=</mo><mo>#</mo><mi>h</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>Y</mi></mrow><mo>¯</mo></mover><mo>=</mo><mo>#</mo><mi>n</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo> </mo><msub><mi>σ</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> </mo><mi>r</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>p</mi><mspace linebreak="newline"/><mi mathvariant="normal">e</mi><mo>)</mo><mo> </mo><mi>T</mi><mi mathvariant="normal">i</mi><mi>p</mi><mi>u</mi><mi>s</mi><mo> </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 X_i i Y_i a partir dels resultats següents:

X_i	Y_i
#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 X_i
b) Calcula la mitjana de Y_i
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 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 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><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>></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>></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 align="center"><mtr><mtd><mn>500</mn><mo>,</mo><mn>520</mn><mo>,</mo><mn>540</mn><mo>,</mo><mn>560</mn><mo>,</mo><mn>580</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>46</mn><mo>,</mo><mn>61</mn><mo>,</mo><mn>35</mn><mo>,</mo><mn>33</mn><mo>,</mo><mn>48</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>540.</mn><mo>,</mo><mn>44.6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>,</mo><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>96.</mn><mo>,</mo><mo>-</mo><mn>0.34</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><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> </mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>X</mi></mrow><mo>¯</mo></mover><mo>=</mo><mo>#</mo><mi>h</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>Y</mi></mrow><mo>¯</mo></mover><mo>=</mo><mo>#</mo><mi>n</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo> </mo><msub><mi>σ</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> </mo><mi>r</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>p</mi><mspace linebreak="newline"/><mi mathvariant="normal">e</mi><mo>)</mo><mo> </mo><mi>T</mi><mi mathvariant="normal">i</mi><mi>p</mi><mi>u</mi><mi>s</mi><mo> </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 (X_i) i l'aparició de càries (Y_i) en un grup d'individus, amb els resultats següents:

X_i	Y_i
#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> </mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>X</mi></mrow><mo>¯</mo></mover><mo> </mo><mo>=</mo><mo>#</mo><mi>X</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>Y</mi></mrow><mo>¯</mo></mover><mo>=</mo><mo> </mo><mo>#</mo><mi>Y</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo> </mo><msub><mi>σ</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> </mo><mi>r</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>p</mi><mspace linebreak="newline"/><mi mathvariant="normal">e</mi><mo>)</mo><mo> </mo><mi mathvariant="normal">e</mi><mi>q</mi><mi>u</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mo> </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 (X_i) i la talla dels fills (Y_i) en un grup d'individus, amb els resultats següents:

X_i	Y_i
#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»

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> </mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>X</mi></mrow><mo>¯</mo></mover><mo> </mo><mo>=</mo><mo>#</mo><mi>X</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>Y</mi></mrow><mo>¯</mo></mover><mo>=</mo><mo> </mo><mo>#</mo><mi>Y</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo> </mo><msub><mi>σ</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> </mo><mi>r</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>p</mi><mspace linebreak="newline"/><mi mathvariant="normal">e</mi><mo>)</mo><mo> </mo><mi mathvariant="normal">e</mi><mi>q</mi><mi>u</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mo> </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 (X_i) amb la producció (Y_i) en cinc camps similars, amb els resultats següents:

X_i	Y_i
#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»

d) Calcula el coeficient de correlació (Pearson) r

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

]]> 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> </mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>X</mi></mrow><mo>¯</mo></mover><mo> </mo><mo>=</mo><mo>#</mo><mi>X</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mover wrs:positionable="false"><mrow wrs:positionable="true"><mi>Y</mi></mrow><mo>¯</mo></mover><mo>=</mo><mo> </mo><mo>#</mo><mi>Y</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo> </mo><msub><mi>σ</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> </mo><mi>r</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>p</mi><mspace linebreak="newline"/><mi mathvariant="normal">e</mi><mo>)</mo><mo> </mo><mi mathvariant="normal">e</mi><mi>q</mi><mi>u</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mo> </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 (X_i) i la talla dels fills (Y_i) en un grup d'individus, amb els resultats següents:

X_i	Y_i
#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 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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> </mo><mi>r</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>p</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mi mathvariant="normal">e</mi><mi>q</mi><mi>u</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">e</mi><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo> </mo><mi>A</mi><mi>l</mi><mi>ç</mi><mi>a</mi><mi mathvariant="normal">d</mi><mi>a</mi><mo> </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 (X_i) #x1 i #x5 es van vendre Y_imòbils en els anys successius amb els resultats següents:

X_i		Y_i
#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.

]]> 1.0000000 0.3333333 0 0 a) equació =#eb) Mòbils =#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>2008</mn><mo>,</mo><mn>2011</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>x2</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>x3</mi><mo>=</mo><mi>x2</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>x4</mi><mo>=</mo><mi>x3</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>x5</mi><mo>=</mo><mi>x4</mi><mo>+</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2016</mn><mo>,</mo><mn>2018</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>A</mi><mo>∉</mo><mfenced close="}" open="{"><mtable 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>4.4993</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>8880.4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2018</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>199.2</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> </mo><mi mathvariant="normal">e</mi><mi>q</mi><mi>u</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">e</mi><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mi>M</mi><mi>ò</mi><mi>b</mi><mi mathvariant="normal">i</mi><mi>l</mi><mi>s</mi><mo> </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_literal"><param name="usecase">false</param><param name="usespaces">false</param></assertion></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">10</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">50 50</data><data name="inputField">popupEditor</data><data name="casSession"/></localData></question>