Standard Deviation about Mean for Continuous Frequency Distributions
The variance ...
Question
The variance of first 'n' natural number is
A
n2+112
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B
n2−112
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C
(n+1)(2n+1)6
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D
None of these
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Solution
The correct option is Cn2−112 By using formula of variance, we have σ2=1nn∑i=1x2i−(1nn∑i=1xi)2 =1n(12+22+⋯+n2)−(1n(1+2+⋯+n))2 =1n⋅n(n+1)(2n+1)6−1n2⋅[n(n+1)2]2 =(n+1)(2n+1)6−(n+1)24