Question

The variance of first 50 even natural numbers is

• A. $\frac{833}{4}$
• B. 833
• C. 437
• D. $\frac{437}{4}$

Answer 1

The correct option is B

833

Here, $\overline{X}=\frac{\sum X_i}{n}=\frac{2+4+6+8+\cdots +100}{50}=\frac{50\times 51}{50}=51$
$[\because \sum 2n=n(n+1),\text{here}n=50]$
$\text{Variance},{\sigma }^2=(\frac{1}{n}\sum X_i^2)-(\overline{X}{)}^2=\frac{1}{50}(2^2+4^2+\cdots +{100}^2)-(51{)}^2=833$