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Q.
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:
Statistics
Solution:
Let $x$ be a set of observations given as
$x = a _{1}, a _{2}, \ldots \ldots \ldots ., a _{ n }$
Then $\bar{x}=\frac{a_{1}+a_{2}+\ldots \ldots . .+a_{n}}{n}$
If now each observation is divided by $\alpha$, then
$\frac{\frac{a_{1}}{\alpha}+\frac{a_{2}}{\alpha}+\ldots \ldots . .+\frac{a_{n}}{\alpha}+10 n}{n}=\frac{\bar{x}}{\alpha}+10$
$=\frac{\bar{x}+10 \alpha}{\alpha}$