4 Marks Each

Question 14 Marks

The information is obtained for $7$ students regarding their marks in Statistics $(X)$ and marks of Economics $(Y)$. The observations of the data were ranked. The sum of squares of differences of ranks was found to be $10.$ If two students got $48$ marks, two students got $40$ marks in Statistics and three students got $55$ marks in Economics, find the rank correlation coefficient.

Answer

$r=0.77$

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Question 24 Marks

The marks obtained by $10$ students in a subject in $80$ marks written examination and $20$ marks oral examination of a university are as follows. Find the rank correlation coefficient.

Marks of written exam	$50$	$55$	$55$	$60$	$65$	$65$	$65$	$60$	$60$	$50$
Marks of oral exam	$11$	$13$	$14$	$16$	$16$	$15$	$15$	$14$	$13$	$13$

Answer

$r=0.74$

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Question 34 Marks

The difference between the marks of the first test and the marks of the second test for a subject of standard $10$ and standard $12$ of six students are given below. Find Karl Pearson's correlation coefficient and write its interpretation.

Difference of Std $10$ marks	$-12$	$-16$	$-8$	$16$	$12$	$8$
Difference of Std $12$ marks	$-10$	$-6$	$-4$	$4$	$6$	$2$

Answer

$r=0.93$, high degree of positive correlation

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Question 44 Marks

Find Karl Pearson's correlation coefficient from the information given below for imports $($in ten million $₹)$ and exports $($in ten million $₹)$ of last seven years in India.

Import $($ten million $₹)$	$18$	$19$	$20$	$21$	$22$	$23$	$24$
Export $($ten million $₹)$	$95$	$88$	$70$	$66$	$57$	$50$	$44$

Answer

$r=-0.99$

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Question 54 Marks

The following data is obtained while studying the height of father $($in cms$)$ and height of his adult son $($in cms$).$ Find the correlation coefficient.

Height of Father $(cm)$	$150$	$163$	$155$	$164$	$163$	$160$	$165$
Height of Son $(cm)$	$156$	$160$	$153$	$160$	$163$	$158$	$163$

Answer

$r=0.82$

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Statistics 4 Marks Each

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