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Question

Mathematics Question on Variance and Standard Deviation

The variance of first 2020 natural numbers is

A

133/4

B

279/12

C

133/2

D

399/4

Answer

133/4

Explanation

Solution

Variance of nn natural numbers
=n2−112=(20)2−112[∵n=20]=\frac{n^{2}-1}{12}=\frac{(20)^{2}-1}{12}[\because n=20]
=400−112=39912=1334=\frac{400-1}{12}=\frac{399}{12}=\frac{133}{4}