The arithmetic mean of a set of observations is X. If each observation is divided by R and then is increased by 10, then the mean of the new series is

# The arithmetic mean of a set of observations is X. If each observation is divided by R and then is increased by 10, then the mean of the new series is

1. A

$\frac{\overline{X}}{\alpha }$

2. B

$\frac{\overline{X}+10}{\alpha }$

3. C

$\frac{\overline{X}+10\alpha }{\alpha }$

4. D

$\alpha \overline{X}+10$

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### Solution:

Let  observations. Then

$\overline{X}=\frac{1}{n}\sum {x}_{i}$

Let ${y}_{i}=\frac{{x}_{i}}{\alpha }+10$ Then

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