Question

The variance of first $50$ even natural numbers is

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

Answer 1

Answer: (B)

Variance $=\frac{\Sigma x_i^2}{N}-(\bar{x}{)}^2$
${\sigma }^2=\frac{2^2+4^2+\dots +100^2}{50}-{\left(\frac{2+4+\dots +100}{50}\right)}^2$
$=\frac{4\left(1^2+2^2+3^2+\dots .+50^2\right)}{50}-(51{)}^2$
$=4\left(\frac{50\times 51\times 101}{50\times 6}\right)-(51{)}^2$
$=3434-2601$
$\Rightarrow {\sigma }^2=833$