If each observation of a raw data whose variance is `sigma` is multiplied by h, then the variance of the new set is

Options

A. `sigma^(2)`
B. `h^(2)sigma`
C. `h sigma^(2)`
D. `h+sigma^(2)`

Answer

B

Explanation

Let `x_(1),x_(2),..,x_(n)` be the raw data. Then,
`sigma^(2)=(1)/(n)underset(i=1)overset(n)(sum)(x_(i)-overline(X))^(2)`.
If each value is multiplied by h, then the values become `hx_(1),hx_(2),..,hx_(n)`. Then AM of the values is
`(hx_(1)+hx_(2)+..+hx_(n))/(n)=h overline(X)`
Therefore, the variance of the new set of values is
`(1)/(n)underset(i=1)overset(n)(sum)(hx_(1)-hoverline(X_(2)))=h^(2)((1)/(n)underset(i=1)overset(n)(sum)(x_(i)-overline(X))^(2))=h^(2)sigma^(2)`