The variance of first n natural numbers is 

The variance of first n natural numbers is 

  1. A

    n2+112

  2. B

    n2-112

  3. C

    (n+1)(2n+1)6

  4. D

    none of these 

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    Solution:

    We have,

    σ2=1ni=1nxi21ni=1nxi2 σ2=1n12+22++n21n(1+2++n)2 σ2=1n×n(n+1)(2n+1)6n+122=n2112

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