Question

The mean of the variates $x_1,x_2,...,x_{n}is\overline{x}$ 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 $\frac{n\overline{x}-x_2+\lambda }{n}$

$\frac{x_1+x_2+...+x_n}{n}=\overline{x}$

$\Rightarrow x_1+x_2+...+x_n=n\overline{x}$

$\Rightarrow x_1+x_2+...+x_n-x_2=n\overline{x}-x_2$

$\Rightarrow x_1+x_3+...+x_n+\lambda =n\overline{x}-x_2+\lambda$

New mean $=\frac{n\overline{x}-x_2+\lambda }{n}$

So, option d is correct.