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Question

If variance of first n natural numbers is 10 and variance of first m even natural numbers is 16, m+n is equal to

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Solution

For n natural number variance is given by
σ2=x2in(xin)2x2in=12+22+32+....n termn=n(n+1)(2n+1)6n
xin=1+2+3+....n termsn=n(n+1)2n
σ2=n2112=10
n=11
Variance of (2,4,6...)=4× variance of (1,2,3,4...)=4×m2112=m213=16m=7
Therefore, n + m = 11 + 7 = 18

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