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Question
The following are the ranks obtained by 10 students in commerce and accountancy are given below:
| Commerce | 6 | 4 | 3 | 1 | 2 | 7 | 9 | 8 | 10 | 5 |
| Accountancy | 4 | 1 | 6 | 7 | 5 | 8 | 10 | 9 | 3 | 2 |
To what extent is the knowledge of students in the two subjects related?
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Solution
| RX | RY | d = RX − RY | d2 |
| 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 |
| ∑d2 = 128 |
N = 11, Σd2 = 128
Rank correlation (ρ) = `1 - (6sum"d"^2)/("N"("N"^2 - 1))`
= `1 - (6 xx 128)/(10(100 - 1))`
= `1 - (6 xx 128)/990`
= 0.224
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