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

Question 19 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 2022Subjective· 3mImportance★★★★★

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Spearman's rank correlation: $\Sigma d^{2}=226$ , $\rho=1-\dfrac{6(226)}{10\times99}\approx-0.37$ .

This applies Spearman's rank correlation coefficient from the TN HSC Class-11 Business Mathematics syllabus.

Step 1 — Compute $d=R_A-R_B$ and $d^{2}$ .

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

Step 2 — Sum of squared differences.

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

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