The mean of a set of observation is ¯¯¯x .If each observation is

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The mean of a set of observation is

¯ ¯ ¯ x

.If each observation is divided by

α α \neq 0

, and then is increased by 10,
then the mean of the new set is

Options:

A . ¯¯¯xα

B . ¯¯¯x+10α

C . ¯¯¯x+10αα

D . α¯¯¯x+10

Answer: Option C
:
C
Let

x_{1}, x_{2} \dots \dots, x_{n}

be n observations.

Then ¯ ¯ ¯ x = \frac{1}{n} \sum x_{i}

let y_{i} = \frac{x_{i}}{α} + 10

¯ ¯ ¯ y = \frac{1}{n} n \sum i y_{i}

And, ¯ ¯ ¯ y = \frac{1}{n} [(n \sum i \frac{x_{i}}{α} + 10. n]

\Rightarrow ¯ ¯ ¯ y = \frac{1}{α} ¯ ¯ ¯ x + 10

= \frac{¯ ¯ ¯ x + 10 α}{α} .

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