Question

By how much should the sum of the $4$ numbers have to be increased, in order for their mean to be increased by $2$?

• A. 2
• B. 4
• C. 6
• D. 8
• E. 16

Answer 1

The correct option is D 8

We have, $\frac{\sum x_i}{4}=\overline{x}$

Let the sum of $4$ numbers be increased by $\delta$.

Then $\frac{\sum x_i+\delta }{4}=\overline{x}+2$

$\Rightarrow \frac{\sum x_i}{4}+\frac{\delta }{4}=\overline{x}+2$

$\Rightarrow \overline{x}+\frac{\delta }{4}=\overline{x}+2$
$\Rightarrow \frac{\delta }{4}=2$ or $\delta =8$