Answer :

Let the observations be x_{1}, x_{2}, x_{3}….x_{20}

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 y_{1}, y_{2}, y_{3}….y_{20}

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 = SD^{2}

So Variance = (2^{2} = 20

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