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The S.D of the first n natural numbers ...

The S.D of the first n natural numbers 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`=(SD)^(2)=(1)/(n)sumx^(2)-((sum x)/(n))^(2), (because overline(x)=(sum x)/(n))`
`=(n(n+1)(2n+1))/(6n)-((n(n+1))/(2n))^(2)=(n^(2)-1)/(12)`
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