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The mean of a set of numbers is overline...

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

A

`overline(X)`

B

`overline(X)+3`

C

`3 overline(X)`

D

`(overline(X))/(3)`

Text Solution

Verified by Experts

The correct Answer is:
D
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)`
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