A synonym for “mean”: the sum of a set of values divided by the number of values. In colloquial language, an **average** is a single number taken as representative of a non-empty list of numbers. Different concepts are used in different contexts. Often “average” refers to the arithmetic mean, the sum of the numbers divided by how many numbers are being taken into count. In statistics, mean, median, and mode are all known as measures of central tendency, and in colloquial usage any of these might be called an **average value**.

The most common type is the arithmetic mean. If *n *numbers are given, each number denoted by *a _{i}* (where

*i*= 1,2, …,

*n*), the arithmetic mean is the sum of the

*a*s divided by

*n*or

#### Some examples of usage

Given a time series, such as daily stock market prices or yearly temperatures, people often want to create a smoother series. This helps to show underlying trends or perhaps periodic behavior. An easy way to do this is the *moving average*: one chooses a number *n* and creates a new series by taking the arithmetic mean of the first *n* values, then moving forward one place by dropping the oldest value and introducing a new value at the other end of the list, and so on. This is the simplest form of moving average. More complicated forms involve using a weighted average. The weighting can be used to enhance or suppress various periodic behavior and there is very extensive analysis of what weightings to use in the literature on filtering. In digital signal processing the term “moving average” is used even when the sum of the weights is not 1.0 (so the output series is a scaled version of the averages). The reason for this is that the analyst is usually interested only in the trend or the periodic behavior.

#### References

Wikipedia. Average. https://en.wikipedia.org/wiki/Average