FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 6.9Taking Ax as 10 and Ay as 15
N = 7
( )^2 ( )^2
200 0x13
r^7
160 0 447 13
10 10−
=
− −
200
160 x 422.8=
200
67648
=
200
=260.09
r = 0.768
6.1.9 Rank Correlation
Rank method for the computation of the coefficient of correlation is based on the rank or the order & not
the magnitude of the variable. Accordingly it is more suitable when the variables can be arranged for e.g.
in case of intelligence or beauty or any other qualitative phenomenon. The ranks may range from 1 to n.
Edward spearman has provided the following formula —
2
2
R 1 6 D
= −N(N 1)−
Where N = Number of pairs of variable X & Y
D = Rank difference
Example 4 :
From the data given belows calculate the rank correlation between x & Y
X 78 89 97 69 59 79 68 57
Y 125 137 156 112 107 136 123 108
Solution:
Table : Computation of Rank Correlation
X Y R 1 R 2 Rank difference D^2
D = R 1 – R 2
78 125 4 4 0 0
89 137 2 2 0 0
97 156 1 1 0 0
69 112 5 6 –1 1
59 107 7 8 –1 1
79 136 3 3 0 0
68 123 6 5 1 1
57 108 8 7 1 1
∑D 0= D 4^2 =