Question

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

Answer 1

x_i= Rank in maths of i^th student

y_i = Rank in accountancy of i^th 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