Question

The mean of $8$ numbers is $25$, if each number is multiplied by $2$ the new mean will be:

• A. $12.5$
• B. $25$
• C. $40$
• D. $50$

Answer 1

The correct option is D $50$

Given, mean of $8$ numbers $=25$.

We know, Mean is given by,

$\text{Mean}=\frac{\text{Sum of the elements}}{\text{Total number of elements}}$ $⟹\overline{x}=\frac{\sum x}{n}$.

Here, number of observations $=8$.

$\Rightarrow 25=\frac{\sum x}{8}$

$\Rightarrow \sum x=25\times 8=200$.

If each number is multiply by $2$, then new sum $=200\times 2=400$.

$\therefore$ New mean $=\frac{400}{8}=50$.

Hence, option $D$ is correct.