Question

If mean of the $n$ observations $x_1,x_2,x_3,\dots ,x_n$ be $\overline{x}$, then the mean of $n$ observations $2x_1+3,2x_2+3,2x_3+3,\dots ,2x_n+3$ is

Answer 1

$\left(\frac{x_1+x_2+......+x_n}{n}\right)=\overline{x}$

$now=\left(\frac{(2x_1+3)+(2x_2+3)+(2x_3+3)+...........+(2x_n+3)}{n}\right)$

$=\left(\frac{(2x_1+2x_2+........+2x_n)+(3+3+.......ntimes)}{n}\right)$

$=2\times \left(\frac{x_1+x_2+......+x_n}{n}\right)+\left(\frac{3\times n}{n}\right)$

$=2\overline{x}+3$