The marks scored by 4 students in Mathematics and Physics are ranked as shown in the table below
| Mathematics | 3 | 4 | 2 | 1 |
| Physics | 4 | 3 | 1 | 2 |
Calculate the Spearmann’s rank correlation coefficient.
- 0.2
- 0.5
-
0.6
- 0.7
The correct answer is: C
Explanation
| Maths (x) | Rank \(r_{x}\) | Physics (y) | Rank \(r_{y}\) | \(d = |r_{x} - r_{y}|\) | \(d^{2}\) |
| 3 | 2 | 4 | 1 | 1 | 1 |
| 4 | 1 | 3 | 2 | 1 | 1 |
| 2 | 3 | 1 | 4 | 1 | 1 |
| 1 | 4 | 2 | 3 | 1 | 1 |
| Total | 4 |
\(\rho = 1 - \frac{6\sum{d^{2}}}{n(n^{2} - 1)}\)
\( 1 - \frac{6 \times 4}{4(4^{2} - 1)} = 1 - \frac{24}{60}\)
= \(1 - 0.4 = 0.6\)