The rank of 10 students of same batch in two subjects A and B are given below. Calculate the rank correlation

Question 31 of 31

The rank of 10 students of same batch in two subjects A and B are given below. Calculate the rank correlation coefficient.

Rank of A	1	2	3	4	5	6	7	8	9	10
Rank of B	6	7	5	10	3	9	4	1	8	2

Puducherry TnboardTamil Nadu HSC First Year (DGE) Commerce Board 2025Subjective· 3mImportance★★★★★

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Compute $d=R_A-R_B$ , then $\sum d^2=226$ ; with $n=10$ , $\rho=1-\dfrac{6(226)}{990}\approx-0.37$ .

Step 1 — tabulate the rank differences $d=R_A-R_B$ and $d^2$ .

$R_A$	$R_B$	$d=R_A-R_B$	$d^2$
1	6	-5	25
2	7	-5	25
3	5	-2	4
4	10	-6	36
5	3	2	4
6	9	-3	9
7	4	3	9
8	1	7	49
9	8	1	1
10	2	8	64

$\sum d^2=25+25+4+36+4+9+9+49+1+64=226.$

Step 2 — apply Spearman's rank correlation formula. …