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The average of n numbers x(1),x(2),x(3),...

The average of n numbers `x_(1),x_(2),x_(3),..,x_(n)` is M. If `x_(n)` is replaced by x', then new average is

A

`M-x_(n)+x'`

B

`(nM-x_(n)+x')/(n)`

C

`((n-1)M+x')/(n)`

D

`(M-x_(n)+x')/(n)`

Text Solution

Verified by Experts

The correct Answer is:
B
`M=(x_(1)+x_(2)+x_(3)..x_(n))/(n)`
`implies nM=x_(1)+x_(2)+x_(3)+..+x_(n-1)+x_(n)`
`implies nM-x_(n)=x_(1)+x_(2)+x_(3)+..+x_(n-1)`
`implies nM-x_(n)+x'=x_(1)+x_(2)+x_(3)+..+x_(n-1)+x'`
`implies (nM-x_(n)+x')/(n)=(x_(1)+x_(2)+x_(3)+..+x_(n-1)+x')/(n)`
`therefore " New average"=(nM-x_(n)+x')/(n)`
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