The following are ranks obtained by 10 students in Commerce and Accountancy. | Commerce | 6 | 4 | 3 | 1 | 2 | 7 | 9 | 8 | 10 | 5 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Accountancy | 4 | 1 | 6 | 7 | 5 | 8 | 10 | 9 | 3 | 2 | Find the Rank Correlation Co-efficient.

> > [!TLDR] > Computing $d = R_1 - R_2$ and $\Sigma d^2 = 128$, Spearman's formula gives $\rho = 1 - \dfrac{768}{990} \approx 0.224$. > > **Step 1 — Rank differences and their squares.** > > | Commerce ($R_1$) | Accountancy ($R_2$) | $d = R_1-R_2$ | $d^2$ | > | --- | --- | --- | --- | > | 6 | 4 | 2 | 4 | > | 4 | 1 | 3 | 9 | > | 3 | 6 | -3 | 9 | > | 1 | 7 | -6 | 36 | > | 2 | 5 | -3 | 9 | > | 7 | 8 | -1 | 1 | > | 9 | 10 | -1 | 1 | > | 8 | 9 | -1 | 1 | > | 10 | 3 | 7 | 49 | > | 5 | 2 | 3 | 9 | > > $$\Sigma d^2 = 4+9+9+36+9+1+1+1+49+9 = 128.$$ > > **Step 2 — Apply Spearman's formula** ($n = 10$). …

The following are ranks obtained by 10 students in – Class 11 Business Mathematics Statistics

Question 23 of 31

The following are ranks obtained by 10 students in Commerce and Accountancy.

Commerce	6	4	3	1	2	7	9	8	10	5
Accountancy	4	1	6	7	5	8	10	9	3	2

Find the Rank Correlation Co-efficient.

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Computing $d = R_1 - R_2$ and $\Sigma d^2 = 128$ , Spearman's formula gives $\rho = 1 - \dfrac{768}{990} \approx 0.224$ .

Step 1 — Rank differences and their squares.

Commerce ( $R_1$ )	Accountancy ( $R_2$ )	$d = R_1-R_2$	$d^2$
6	4	2	4
4	1	3	9
3	6	-3	9
1	7	-6	36
2	5	-3	9
7	8	-1	1
9	10	-1	1
8	9	-1	1
10	3	7	49
5	2	3	9

$\Sigma d^2 = 4+9+9+36+9+1+1+1+49+9 = 128.$

Step 2 — Apply Spearman's formula ( $n = 10$ ). …

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