Question

The arithmetic mean of set of observations is $\overline{x}$ If each observation is divided by $\alpha$ and then is increased by $10$, then the mean of new series is

• A. $\frac{\overline{x}}{\alpha }$
• B. $\frac{\overline{x}+10}{\alpha }$
• C. $\frac{\overline{x}+10\alpha }{\alpha }$
• D. $\alpha \overline{x}+10$

Answer 1

The correct option is C

$\frac{\overline{x}+10\alpha }{\alpha }$

Let $x_1,x_2,.......x_n$ be $n$ observations.

then $\overline{x}=\frac{1}{n}\sum x_i$

$\therefore \frac{\overline{x}}{\alpha }+10$ is required mean.