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Question

If $$\displaystyle \sum d_i^2 = 25$$, $$n = 6$$ find rank correlation coefficient where $$d_i$$ is the difference between the ranks of $$i^{th}$$ values.


Solution

Given that:
$$\sum di^2=25$$, $$n=6$$

The rank coefficient is given by
$$r=1-\dfrac{6\sum di^2}{n(n^2-1)}$$
$$r=1-\dfrac{6\times 25}{6(6^2-1)}$$
$$r=1-\dfrac{5}{7}$$
$$r=\dfrac{2}{7}.$$

This is the required solution.

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