Question

The mean of the series $x_1,x_2,x_3,.......,x_n$ is $\overline{x}$. If $x_2$ is replaced by $\lambda$, then the new mean is

• A. $\overline{x}-x_2+\lambda$
  
• B. $\frac{\overline{x}-x_2-\lambda }{n}$
  
• C. $\frac{(n-1)\overline{x}+\lambda }{n}$
  
• D. $\frac{n\overline{x}-x_2+\lambda }{n}$

Answer 1

The correct option is D $\frac{n\overline{x}-x_2+\lambda }{n}$

$\overline{x}=\frac{x_1+x_2+x_3+....+x_n}{n}\therefore n\overline{x}=x_1+x_2+....+x_n\Rightarrow x_1+x_3+....+x_n=n\overline{x}-x_{2}Newmean=\frac{x_1+\lambda +x_3+....+x_n}{n}\frac{n\overline{x}-x_2+\lambda }{n}$