Given, The variance of 20 observations is 4.

To Find: Find the variance of resulting observations.

Explanation: Let Assume, x₁,x₂,x₃,…,x₂₀ be the given observations.

So, Variance (X) = 5 (Given)

X =

Now, Let u₁,u₂,…u₂₀ be the new observation,

When we multiply the new observation by 2, then

U_i=2x_i (for i=1,2,3…,20) ---(i)

Now,

Mean =

Mean =

Since, u_i- = 2x_i

2(x_i )

Now, (u_i-)² = (2(x_i ))²

4(x_i )²

Comparing Both the observations,

Variance (U) =4×Variance (X)

4×5

20

Hence, The variance of new observations is 20.