Question

The mean of n numbers $x_1,x_2$...$x_n$ is M If $x_1$ is replaced by $x^{\prime }$ then the new mean is

• A. $M-x_1+x^{\prime }$
• B. $\frac{(n-1)M+x^{\prime }}{n}$
• C. $M+\frac{x^{{}^{\prime }}-x_1}{n}$
• D. $\frac{M-x_1+x^{\prime }}{n}$

Answer 1

The correct option is C $M+\frac{x^{{}^{\prime }}-x_1}{n}$

$\frac{x_1+x_2+x_3+........x_n}{n}=M$

$\Rightarrow x_1+x_2+x_3+........x_n=Mn$

Adding $x^{{}^{\prime }}$ and substituting $x_1$ both side we get

$\Rightarrow x_2+x_3+........x_n+x^{{}^{\prime }}=Mn+x^{{}^{\prime }}-x_1$

Then mean =$\frac{x_2+x_3+........x_n+x^{{}^{\prime }}}{n}=\frac{Mn+x^{{}^{\prime }}-x_1}{n}=M+\frac{x^{{}^{\prime }}-x_1}{n}$