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.
-
A.
0.2 -
B.
0.5 -
C.
0.6 -
D.
0.7
Correct Answer: Option 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{6sum{d^{2}}}{n(n^{2} – 1)})
( 1 – frac{6 times 4}{4(4^{2} – 1)} = 1 – frac{24}{60})
= (1 – 0.4 = 0.6)