# notes Mean (changes)

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# Mean

## Definition

###### Definition

The mean of a population or a sample of a population is a measure of central tendency. For data $x_i$, it is defined as

$\bar{x} = \frac1n \sum x_i$

## Properties

### Behaviour Under Coding

Suppose that the data $x_i$ is coded as $y_i$ via the following formula in which $a$ and $b$ are constant:

$y_i = a x_i + b$

Then the means of $y_i$ and $x_i$ are related via:

$\bar{y} = a \bar{x} + b$

=average(<range>)