The mean of a set of numbers is `overline(X)`. If each number is divided by 3, then the new mean is

Options

A. `overline(X)`
B. `overline(X)+3`
C. `3 overline(X)`
D. `(overline(X))/(3)`

Answer

D

Explanation

Let `x_(1),x_(2),..,x_(n)` be n numbers. Then `overline(X)=(1)/(n) underset(i=1)overset(n)sum x_(i)`.
If each number is divided by 3, then the new mean `overline (Y)` is given by
`overline(Y)=(1)/(n)underset(i=1)overset(1)sum((x_(i))/(3))=(1)/(3)((1)/(n)underset(i=1)overset(n)sum x_(i))=(overline(X))/(3)`