The standard deviation of 20 observations is √5. If each observation is multiplied by 2, find the standard deviation and variance of the resulting observations.

Let the observations be x₁, x₂, x₃….x₂₀

Given SD =

Formula for SD =

Where N = 20, SD =

If each observation is multiplied by 2, we get new set of observations.

Let the new observations be y₁, y₂, y₃….y₂₀

New Standard Deviation SD’ =

We know that and

But y_i = 2x_i

Therefore,

Substituting in the SD’ formula,

SD’ =

=

= 2 × SD = 2

Formula relating SD and Variance is Variance = SD²

So Variance = (2² = 20