Question

The mean of the series $x_1,x_2,.....x_{n}is\overline{x}.If{x}_2$ is replaced by $\lambda ,$ then the new mean is

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

Answer 1

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

$\because \frac{x_1+x_2+x_3+----+x_n}{n}=\overline{x}$
$x_1+x_2+x_3+....+x_n=n\overline{x}$
$\Rightarrow x_1+x_3+....+x_n=n\overline{x}-x_2$ ....(1)
Now, $x_2$ is replaced by $\lambda$
New Mean = $\frac{x_1+\lambda +x_3+----+x_n}{n}$
$=\frac{(x_1+x_3+----+x_n)+\lambda }{n}$
$=\frac{n\overline{x}+\lambda -x_2}{n}$ by (1)