Q53 / 150 · MHT CET 2024 (04 May Shift 1) · Mathematics

The variance of first 50 even natural numbers is

  • Correct answer
    A
    833
  • B
    473
  • C
    $\frac{437}{4}$
  • D
    $\frac{833}{4}$

Solution

$\begin{aligned} & \text { Variance }=\frac{\sum x_{\mathrm{i}}^2}{\mathrm{n}}-(\bar{x})^2 \\ & =\frac{\left(2^2+4^2+\ldots+100^2\right)}{50}-\left(\frac{2+4+\ldots+100}{50}\right)^2 \\ & =\frac{4\left(1^2+2^2+\ldots .+50^2\right)}{50}-(51)^2 \\ & =4\left(\frac{50 \times 51 \times 101}{50 \times 6}\right)-(51)^2 \\ & =3434-2601 \\ & =833\end{aligned}$

Hence, the correct answer is option: 'A'.

More Statistics Questions