# The variance of 2

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

Ui=2xi (for i=1,2,3…,20) ---(i)

Now,

Mean =  Mean = Since, ui- = 2xi 2(xi )

Now, (ui- )2 = (2(xi ))2

4(xi )2

Comparing Both the observations,  Variance (U) =4×Variance (X)

4×5

20

Hence, The variance of new observations is 20.

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