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Question

If variance of the first n natural numbers is 10, then the value of n is

A
11
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B
6
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C
3
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D
15
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Solution

The correct option is A 11
Variance, σ2=x2in(xin)2
For first n natural numbers,
x2in=12+22+32++n2nx2in=n(n+1)(2n+1)6nx2in=(n+1)(2n+1)6

xin=1+2+3++nnxin=n(n+1)2n=n+12
Now, σ2=(n+1)(2n+1)6(n+1)24
σ2=(n+1)(2n2)24n2112=10n=11

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