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Coefficient of rank correlation between x and y is 0.5 and `sumd_i^2`= 42. Assuming that no ranks are repeated, find the number of pairs of observations.

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#### Solution

`r=0.5`

`sumd_i^2=42`

`n=?`

`R=1-(6sumd_i^2)/(n(n^2-1))`

`0.5=1-(6(42))/(n(n^2-1))`

`=1-252/(n(n^2-1))`

`252/(n(n^2-1))=1-0.5`

`252/(n(n^2-1))=0.5`

`(n(n^2-1))=252/0.5xx10/10`

`=504`

put n=10

`10(99)=990`

put n=9

`9(80)=720`

put n=8

`8(63)=504`

`therefore n=8`

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