Question

Following are the rank obtained by 10 students in two subjects , Statistics and Mathematics . To what extent the knowledge of the students in the two subjects is related?

Statistics	1	3	3	4	5	6	7	8	9	10
Mathematics	2	4	1	5	3	9	7	10	6	8

• A. 0.76
• B. 0.66
• C. 0.56
• D. 0.48

Answer 1

The correct option is A 0.76

Statistic $\left(X\right)$	Mathematics $\left(Y\right)$	$XY$	$X^2$	$Y^2$
1 3 3 4 5 6 7 8 9 10	2 4 1 5 3 9 7 10 6 8	2 12 3 20 15 54 49 80 54 80	1 9 9 16 25 6 49 64 81 100	4 16 1 25 9 81 49 100 36 64

$\sum X=56,\sum Y=55,\sum XY=369,\sum X^2=390,\sum Y^2=385$

$N=10$

Cov$(x,y)=\frac{\sum XY}{N}-\frac{\sum X}{N}.\frac{\sum Y}{N}=\frac{369}{10}-\frac{56}{10}.\frac{55}{10}=6.1$

${\sigma }_x=\sqrt{\frac{\sum X^2}{N}-{\left(\frac{\sum X^2}{N}\right)}^2}=\sqrt{\frac{390}{10}-{\left(\frac{56}{10}\right)}^2}=2.76$

${\sigma }_y=\sqrt{\frac{\sum Y^2}{N}-{\left(\frac{\sum Y^2}{N}\right)}^2}=\sqrt{\frac{385}{10}-{\left(5.5\right)}^2}=2.87$

$r=\frac{Cov(x,y)}{{\sigma }_x.{\sigma }_y}=\frac{6.1}{2.87\times 2.76}=0.77$