Question

The means of a set of numbers is $\overline{X}$. If each number is divided by $3$, then the new mean is

• A. $\overline{X}$
• B. $\overline{X}+3$
• C. $3\overline{X}$
• D. $\frac{\overline{X}}{3}$

Answer 1

The correct option is D $\frac{\overline{X}}{3}$

Let $x_1,x_2,x_3.................x_n$ are the set of $X$.
$\Rightarrow \frac{x_1+x_2+x_3+........................x_n}{n}=\overline{X}......\left(1\right)$

New set of data's are, $\frac{x_1}{3},\frac{x_2}{3},\frac{x_3}{3},.............\frac{x_3}{3}$
$\therefore$ New mean $=\frac{\frac{x_1}{3}+\frac{x_2}{3}+\frac{x_3}{3}+..............+\frac{x_n}{3}}{3}$
$=\frac{x_1+x_2+x_3+........................x_n}{3n}=\frac{\overline{X}}{3}$ (using (1))