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The variance of first n natural number i...

The variance of first n natural number is:

A

`(n^(2)-1)/(12)`

B

`(n^(2)-1)/(6)`

C

`(n^(2)+1)/(6)`

D

`(n^(2)+1)/(12)`

Text Solution

Verified by Experts

The correct Answer is:
A
Variance `=(S.D)^(2)=1/n sumx^(2)-((sumx)/n)^(2) [therefore x=(sumx)/(n)]`
`=(n(n+1)(2n+1))/(6n)-((n(n+1))^(2)/(2n))=(n^(2)-1)/(12)`
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