Question

If the mean of the set of numbers $x_1,x_2,x_3,\cdots x_n$ is $\overline{x}$ then the mean of numbers $x_i+2i$
$\forall i=1,2,3,\cdots n$ such that $1\le i\le n,$ is

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

Answer 1

Answer: (B)

$\overline{x}+n+1$

Required mean $=\frac{{\sum }_{i=1}^{i=n}(x_i+2i)}{n}=\frac{\sum x_i}{n}+2.\frac{\sum n}{n}=\overline{x}+n+1$