The average of n numbers  x1,x2,…,xn  is M. If  xn is replaced by  x’ , then the new average is

# The average of n numbers   is $M.$ If  is replaced by  $x\text{'}$ , then the new average is

1. A

$\frac{M-{x}_{n}+{x}^{\mathrm{\prime }}}{n}$

2. B

$\frac{\left(n-1\right)M+{x}^{\mathrm{\prime }}}{n}$

3. C

$\frac{nM-{x}_{n}+{x}^{\mathrm{\prime }}}{n}$

4. D

$M-{x}_{n}+{x}^{\mathrm{\prime }}$

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### Solution:

We have,

$M=\frac{{x}_{1}+{x}_{2}+\dots +{x}_{n}}{n}$

$\begin{array}{l}⇒ {x}_{1}+{x}_{2}+\dots +{x}_{n-1}+{x}_{n}=nM\\ ⇒ {x}_{1}+{x}_{2}+\dots +{x}_{n-1}=nM-{x}_{n}\end{array}$

Let M' be the average of

[Using (i)]

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