Question

If the variance of 1, 2, 3, 4, 5, ...,10 is $\frac{33}{4}$, then the standard deviation of 3, 6, 9, 12, ...33 is ______________.

Answer 1

Since Variance of 1, 2, 3, 4, 5, .......10 is $\frac{33}{4}$.
Using if Variance of x₁, x₂, .......x_n is $\sigma$ then Variance of ax₁, ax₂, .......ax_n is a²$\sigma$²
$\therefore$ Variance of 3, 6, 9, .......30
i.e Variance of 3(1), 3(2), 3(3), .......3(10) is (3)² Variance (1, 2, 3, ......10)

$\mathrm{i}.\mathrm{e}9\times \frac{33}{4}=\frac{9\times 33}{4}$
$\therefore \mathrm{Standard}\mathrm{deviation}\mathrm{of}3,6,9,.......30\mathrm{is}\sqrt{\frac{9\times 33}{4}}=\frac{3}{2}\sqrt{33}$