Question

The marks obtained by the students in physics and in mathematics are as follows.

Marks in Physics	35	23	47	17	10	43	9	6	28
Marks in Mathematics	30	33	45	23	8	49	12	4	31

Compute of correlation of ranks.

• A. 0.2
• B. 0.3
• C. 0.7
• D. 0.9

Answer 1

The correct option is D 0.9

Marks of Physics $\left(X\right)$	Marks in Maths$\left(Y\right)$	$XY$	$X^2$	$Y^2$
35 23 47 17 10 43 9 6 28	30 33 45 23 8 49 12 4 31	1050 759 2115 391 80 2107 108 24 868	1225 529 2209 289 100 1849 81 35 784	900 1089 2025 529 64 2401 144 16 961

$\sum X=218,\sum Y=235,\sum XY=7502,\sum X^2=7102,\sum Y^2=8129$

$N=09$

Cov$(x,y)=\frac{\sum XY}{N}-\frac{\sum X}{N}.\frac{\sum Y}{N}=\frac{7502}{09}-\frac{218}{9}.\frac{235}{9}=201.08$

${\sigma }_x=\sqrt{\frac{\sum X^2}{N}-{\left(\frac{\sum X^2}{N}\right)}^2}=\sqrt{\frac{7102}{09}-{\left(\frac{218}{09}\right)}^2}=14.22$

${\sigma }_y=\sqrt{\frac{\sum Y^2}{N}-{\left(\frac{\sum Y^2}{N}\right)}^2}=\sqrt{\frac{8129}{09}-{\left(\frac{235}{9}\right)}^2}=14.88$

$r=\frac{Cov(x,y)}{{\sigma }_x.{\sigma }_y}=\frac{201.08}{14.22\times 14.88}=\mathrm{0..95}$