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प्रश्न
The ranks of the 10 students in Mathematics and Accountancy are as follows :
Two numbers given in the brackets denote the ranks of the students in Mathematics and Accountancy respectively.
(1. 1). (2. 10). (3. 3). (4. 4). (5. 5). (6. 7). (7. 2). (8. 6). (9. 8). (10. 9)
Calculate the rank correlation coefficient
उत्तर
xi= Rank in maths of ith student
yi = Rank in accountancy of ith student
| Rank in maths | Rank in accountancy | di = (xi - yi) | `d_i^2` |
| 1 | 1 | 0 | 0 |
| 2 | 10 | -8 | 64 |
| 3 | 3 | 0 | 0 |
| 4 | 4 | 0 | 0 |
| 5 | 5 | 0 | 0 |
| 6 | 7 | -1 | 1 |
| 7 | 2 | 5 | 25 |
| 8 | 6 | 2 | 4 |
| 9 | 8 | 1 | 1 |
| 10 | 9 | 1 | 1 |
| `Sigmad_i^2` = 96 |
Here n = 10, `Sigmad_i^2` = 96
Rank correlation coefficient
R = `1 - (6Sigmad_i^2)/(n(n^2 - 1))`
= 1 - `(6(96))/(10(10^2 - 11))`
= 1 - `576/990`
= 1 - 0.5818
= 0.4182
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