Question

The mean of $20$ numbers is $9$. If $3$ is added to every number, what will be the new mean?

• A. $9$
• B. $12$
• C. $27$
• D. $15$

Answer 1

The correct option is B $12$

Given, mean of $20$ numbers is $9$.

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 $=20$.

$\Rightarrow 9=\frac{\sum x}{20}$

$\Rightarrow \sum x=9\times 20=180$.

If $3$ is added to the every number, then $\sum x=180+(20\times 3)=240$.

$\therefore$ New Mean $=\frac{240}{20}=12$.

Hence, option $B$ is correct.