Let the observations are x₁, x₂, x₃, x₄, …, x₂₀

and Let mean =

Given: Variance = 5 and n = 20

We know that,

Putting the given values, we get

or …(i)

It is given that each observation is multiplied by 2, we get new observations

Let the new observation be y₁, y₂, y₃, …, y₂₀

where y_i = 2(x_i) …(ii)

or …(iii)

Now, we find the variance of new observations

Now, we calculate the value of

We know that,

[from eq. (ii)]

…(iv)

Putting the value of eq. (iii) and (iv) in eq. (i), we get

So,

= 20