Question

The marks obtained by nine students in physics and Mathematics are given below:

Physics	48	60	72	62	56	40	39	52	30
Mathematics	62	78	65	70	38	54	60	32	31

calculate spearman's coefficient.

• A. $r=0.66$
• B. $r=0.32$
• C. $r=0.53$
• D. $r=0.28$

Answer 1

The correct option is A $r=0.66$

Descending order arranged data will be as follows:

Physics: $72,62,60,56,52,48,40,39,30$

MAthematics: $78,70,65,62,60,54,38,32,31$

Thus data will be

Physics$\left(P\right)$	Mathematics $\left(M\right)$	Rank $\left(P\right)$	Rank $\left(P\right)$	$|d|$	$d^2$
48 60 72 62 56 40 39 52 30	62 78 65 70 38 54 60 32 31	6 3 1 2 4 7 8 5 9	4 1 3 2 7 6 5 8 9	2 2 2 0 3 1 3 3 0	4 4 4 0 9 1 9 9 0

$n=9,\sum d^2=40$

$r=1-\frac{6\sum d^2}{n(n^2-1)}=1-\frac{40\times 6}{9(9^2-1)}=1-\frac{240}{720}=0.66$