Question

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

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

Answer 1

Answer: (C)

Let $x$ be a set of observations given as
$x=a_1,a_2,\dots \dots \dots .,a_n$
Then $\bar{x}=\frac{a_1+a_2+\dots \dots ..+a_n}{n}$
If now each observation is divided by $\alpha$, then
$\frac{\frac{a_1}{\alpha }+\frac{a_2}{\alpha }+\dots \dots ..+\frac{a_n}{\alpha }+10n}{n}=\frac{\bar{x}}{\alpha }+10$
$=\frac{\bar{x}+10\alpha }{\alpha }$