Question

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. $\frac{nM-x_n+x^{!}}{n}$
• C. $\frac{(n-1)M+x^{!}}{n}$
• D. $\frac{M-x_n+x^{!}}{n}$

Answer 1

The correct option is B $\frac{nM-x_n+x^{!}}{n}$

$M=\frac{x_1+x_2+x_3.........x_n}{n}$
$nM=x_1+x_2+x_3+........x_{n-1}$
$\frac{nM-x_n+x^{!}}{n}=\frac{x_1+x_2+x_3+.......x_{n-1}+x^{!}}{n}$
$\therefore Newaverage=\frac{nM-x_n+x^{!}}{n}$