Question

If the mean of the set of numbers $x_1,x_2.x_3,.....,x_n$ is $\overline{x}$, then the mean of the numbers $x_1+2i,1\le i\le n$ is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

We know that $\overline{x}=\frac{\sum _{i=1}^n{x}_1}{n}i.e.,\sum _{i=1}^n{x}_1=n\overline{x}$
$\therefore \frac{\sum _{i=1}^n{x}_1+2_i}{n}=\frac{\sum _{i=1}^n{x}_1+2\sum _{i=1}^n{x}_1}{n}=\frac{n\overline{x}+2(1+2+....+n)}{n}$
$=\frac{n\overline{x}+2\frac{n(n+1)}{2}}{n}=\overline{x}+n+1$