The average of n numbers x1,x2,x3,…,xn is M. If xn is replaced by x', then new average is

A
$M - x_{n} + x^{'}$
B
$\frac{nM - x_{n} + x^{'}}{n}$
C
$\frac{(n - 1) M + x^{'}}{n}$
D
$\frac{M - x_{n} + x^{'}}{n}$

Solution:

$\begin{array}{l} M = \frac{x_{1} + x_{2} + x_{3} \dots \dots x_{n}}{n} \\ \Rightarrow nM = x_{1} + x_{2} + x_{3} + \dots + x_{n - 1} + x_{n} \\ \Rightarrow nM - x_{n} = x_{1} + x_{2} + x_{3} + \dots + x_{n - 1} \\ \Rightarrow nM - x_{n} + x^{'} = x_{1} + x_{2} + x_{3} + \dots + x_{n - 1} + x^{'} \\ \Rightarrow \frac{nM - x_{n} + x^{'}}{n} = \frac{x_{1} + x_{2} + x_{3} + \dots + x_{n - 1} + x^{'}}{n} \end{array}$
$∴$ New average $= \frac{nM - x_{n} + x^{'}}{n}$

The average of n numbers $x_{1}, x_{2}, x_{3}, \dots, x_{n}$ is M. If $x_{n}$ is replaced by x', then new average is

Solution:

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