# Averages: Measures of central tendency

An **average** is a statistical method to summarize the central tendency, as opposed to the spread, of a set of numerical data. The three types of averages are mean, median, and mode.

## Arithmetic mean

The **arithmetic mean**, or simply **mean**, is sum of all numbers in a collection divided by the number of numbers in that collection. This is what is typically meant when someone refers to an "average" without specifying which type of average.

$A={\frac {1}{n}}\sum _{i=1}^{n}a_{i}={\frac {a_{1}+a_{2}+\cdots +a_{n}}{n}}$

Means works best when the range is relatively symmetrical and unlikely to contain outliers, which can skew the data beyond usefulness.

## Median

The **median** of a collection of numbers is the middle number when that collection is sorted. If there are two middle numbers (i.e. if the collection has an even number of numbers), then the median is the mean of those two numbers.

The median is most useful when the distribution of values is skewed or contains outliers.

## Mode

The **mode** is the most frequently repeated number in a collection. If two or more values "tie" for being most common, then the mode is undefined.

## Deeper Knowledge on Averages: Measures of Central Tendency

### Dispersions: Measures of Spread

Usage and calculations for range, standard deviation, and variance on a set of numbers

### Interquartile Range (IQR)

How to find the interquartile range (IQR) of a number collection

## Broader Topics Related to Averages: Measures of Central Tendency

### Dispersions: Measures of Spread

Usage and calculations for range, standard deviation, and variance on a set of numbers

### Statistics

The analysis of numerical data