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Question

Find the coefficient of rank correlation between the marks obtained in Mathematics and those in Statistics by 10 students of a class.
Marks in Mathematics 12 18 32 18 25 24 25 40 38 22
Marks in Statistics 16 15 28 16 24 22 25 36 34 19

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Solution

Marks in Maths Marks in Statistics R1 R2 D = R1−R2 D2
12
18
32
18
25
24
25
40
38
22
16
15
28
16
24
22
25
36
34
19
1
2.5
8
2.5
6.5
5
6.5
10
9
4
2.5
1
8
2.5
6
5
7
10
9
4
-1.5
1.5
0
0
0.5
0
-0.5
0
0
0
2.25
2.25
0
0
0.25
0
0.25
0
0
0
ΣD2=5

Here, N = 10
m1= m2 = m3 = 2

rk=1- 6ΣD2+112m13-m1+112m23-m2+112m33-m3N3-Nor, rk=1- 65+1128-2+1128-2+1128-2990rk=0.960

Hence, the value of rank correlation coefficient is 0.960.

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