## Arithmetic Mean

### Introduction

In mathematics and statistics, the ** arithmetic mean**, or simply the mean or average when the context is clear, is the central tendency of a collection of numbers taken as the sum of the numbers divided by the size of the collection.

### Definition

Suppose we have sample space {a_{1} , ... , a_{n}}. Then the arithmetic mean A is defined via the equation:

If the list is a statistical population, then the mean of that population is called a ** population mean**. If the list is a statistical sample, we call the resulting statistic a

**.**

*sample mean*The arithmetic mean of a variable is often denoted by a bar, for example (read "x bar") would be the mean of the sample space X.

### References & Resources

- http://en.wikipedia.org/wiki/Arithmetic_mean

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