Introduction to statistics

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Question

The variance of first 50 even natural numbers is

Moderate

Solution

We know that $Var (a X) = a^{2} Var (X)$
$∴ Var (2, 4, 6, \dots, 100) = 4 Var (1, 2, 3, \dots, 50)$
$= 4 (\frac{50^{2} - 1}{12}) [∵ Var (1, 2, \dots, n) = \frac{n^{2} - 1}{12}]$
= 833

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