Question

Given two subjects A and B, if the ranks of subject A are 1,2,3,4 & 5 and of subject B are 5,4,3,2 & 1. The value of R will be​

Answer 1

Given :

two subjects A and B, if the ranks of subject A are 1,2,3,4 & 5 and of subject B are 5,4,3,2 & 1.

To Find :  R The Rank correlation coefficient

 

Solution:

R1         1          2         3          4           5

R2        5         4         3          2            1

d          -4        -2        0          2            4

d²         16        4         0          4           16

∑d²   = 16  + 4 + 0 + 4 + 16 = 40  

rank correlation coefficient    = 1   - 6  ∑ (di)² / (n(n² - 1))

n = 5

∑ (di)²  = sum of squares of the differences in ranks = 40

rank correlation coefficient  =  1  - 6 ( 40) / ( 5 ( 5² - 1))

= 1  - 240 / 5(24)

= 1  - 2

= -1

The Rank correlation coefficient  is  -1  

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