Question

The mean of a set of observation is $\overline{x}$. If each observation is divided by $\alpha [\alpha \ne 0$], and then is increased by 10,
then the mean of the new set is:

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Let $x_1,x_2\dots \dots ,x_n$ be n observations.
$Then,\overline{x}=\frac{1}{n}\sum x_i$
$let{y}_i=\frac{x_i}{\alpha }+10$
$Newmean=\overline{y}=\frac{1}{n}\sum _i^n{y}_i$
$And,\overline{y}=\frac{1}{n}\left[\right(\sum _i^n\frac{x_i}{\alpha }+10.n]$
$\Rightarrow \overline{y}=\frac{1}{\alpha }\overline{x}+10$
$=\frac{\overline{x}+10\alpha }{\alpha }$