Question

The mean of a set of observations is $\bar{x}$. If each observation is divided by $\alpha,(\alpha \neq 0)$ and then is increased by $10$ , then the mean of the new set is

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

Answer 1

Answer: (C)

Let the set of $n$ observations $x _1, x _2, \ldots \ldots x _{ n }$
$\therefore \quad \overline{ x } =\frac{\Sigma x _1}{ n }$
Mean of new set $=\frac{\Sigma\left(\frac{ x _1}{\alpha}+10\right)}{ n }=\frac{1}{\alpha} \frac{\sum x _1}{ n }+\frac{10 n }{ n }=\frac{\overline{ x }+10 \alpha}{\alpha}$