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