Question

If the rank correlation coefficient is `2/3` and `Σ"d"_1^2` = 55` , then find the number of  pairs of observations. (Assume that no rank is repeated.) 

Answer 1

`Σ"d"_i^2` = 55`

∴ `"R" = + 2/3`

But `"R" = 1 - (6Σ"d"_i^2)/(n(n^2 - 1))`

∴ `+2/3 = 1 - (6 xx 55)/(n(n^2 - 1))`

∴ `+(6 xx 55)/(n(n^2 - 1)) = 1 - 2/3`

∴ `(6 xx 55)/(n(n^2 - 1)) = 1/3`

∴ `n(n^2 - 1) = 6 xx 55 xx 3`

= `2 xx 3 xx 11 xx 5 xx 3`

`(n + 1)(n - 1)n = 11 xx 10 xx 9`

⇒ n = 10