Question

If the mean of a set of observations $x_1,x_2,...,x_n$ is $\overline{X}$, then the mean of the observations $x_i+2i;i=1,2,...,n$ is

• A. $\overline{X}+2$
• B. $\overline{X}+2n$
• C. $\overline{X}+(n+1)$
• D. $\overline{X}+n$

Answer 1

The correct option is C $\overline{X}+(n+1)$

We have,
$\overline{X}=\frac{\sum _{r=1}^{r=n}{x}_i}{n}$
Also,
$\overline{X^{\prime }}=\frac{\sum _{r=1}^{r=n}{(x}_i+2i)}{n}$
$\overline{X^{\prime }}=\overline{X}+\frac{2\sum _{r=1}^{n}i}{n}$
$\overline{X^{\prime }}=\overline{X}+n+1$