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Calculate rank correlation coefficient whose marks in statistics and economics are given as follows:

Stats: 41 45 70 45 30 67 70

Eco: 40 55 47 65 55 71 55

Rank in stats: 6, 4.5 , 1.5, 4.5, 7, 3, 1.5

Rank in eco: 7 4 6 2 4 1 4

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1 Answer

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xi yi di = (xi - yi) di2
6 7 -1 1
4.5 4 0.5 0.25
1.5 6 -4.5 20.25
4.5 2 2.5 6.25
7 4 3 9
3 1 2 4
1.5 4 -2.5 6.25
\(\sum\)di2 = 47

We have \(\sum\)di2 = 47, n = 7

Spearman's rank correction coefficient = \(\cfrac{1-6\sum d_i^2}{n(n^2-1)}\) 

\(\cfrac{1-6\times47}{7(7^2-1)}\) = \(\cfrac{1-282}{336}\) 

= 0.1607

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