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 $\frac{n\overline{X}-x_2+\lambda }{n}$

We have given, $\overline{X}=\frac{x_1+x_2+x_3+.................+x_n}{n}$
Now $x_2\to \lambda$
$\therefore \overline{X_{new}}=\frac{x_1+\lambda +x_3+.................+x_n}{n}$
$=\frac{(x_1+x_2+x_3+.................+x_n)+(\lambda -x_2)}{n}=\overline{X}+\frac{\lambda -x_2}{n}=\frac{n\overline{X}-x_2+\lambda }{n}$