The variance of `20` observations is `5.` If each observation is multiplied by `2,` find the new variance of the resulting observations.

Options

A. `20`
B. `30`
C. `40`
D. `50`

Answer

A

Explanation

given that ` n= 20`

let the mean be `bar x`

individual observation `x_i`

variance be `sigma^2` that is `5`

now, as we know that,

`bar x= (sumx_i)/n`

`sigma^2 = (sum(x_i- bar x)^2)/n = 1/n*sumx_i^2 - (bar x)^2`

now let the new observation is `y_i = k*x_i` and no of observation is n

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