MHT CET · Maths · Statistics
The variance of first 50 even natural numbers is
- A 833
- B 473
- C \(\frac{437}{4}\)
- D \(\frac{833}{4}\)
Answer & Solution
Correct Answer
(A) 833
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Variance }=\frac{\sum x_{\mathrm{i}}^2}{\mathrm{n}}-(\bar{x})^2 \\ & =\frac{\left(2^2+4^2+\ldots+100^2\right)}{50}-\left(\frac{2+4+\ldots+100}{50}\right)^2 \\ & =\frac{4\left(1^2+2^2+\ldots .+50^2\right)}{50}-(51)^2 \\ & =4\left(\frac{50 \times 51 \times 101}{50 \times 6}\right)-(51)^2 \\ & =3434-2601 \\ & =833\end{aligned}\)
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