Question

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

• A. $\overline{x}+2n$
• B. $\overline{x}+n+1$
• C. $\overline{x}+3n$
• D. $\overline{x}+n$

Answer 1

The correct option is B $\overline{x}+n+1$

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

New Mean $=\frac{x_1+2+x_2+4+...x_n+2n}{n}$

$=\frac{x_1+x_2+......x_n}{n}+\frac{2+4+6+...2n}{n}$

$=\overline{x}+\frac{n(n+1)}{n}\because [1+2+.......n=\frac{n(n+1)}{2}]$

$\overline{x}+n+1$

$B$ is correct.