Mean

In statistics, mean has two related meanings:

Arithmetic mean

The arithmetic mean is the "standard" average, often simply called the "mean".

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: ar{x} = {1 over n} sum_{i=1}^n{x_i}

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Do not confuse the mean with the median or mode! The mean is the arithmetic average of a set of values, or distribution; however, for skewed distributions, the mean is not the same as the middle value (median), or most likely (mode). For example, mean income is skewed upwards by a small number of people with very large incomes, so that the majority have an income lower than the mean. By contrast, the median income is the level at which half the population is below and half is above. The mode income is the most likely income, and favors the larger number of people with lower incomes. The median or mode are often more intuitive measures of such data.

Related Topics:
Median - Mode - Skewed

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That said, many skewed distributions are best described by their mean - such as the Exponential and Poisson distributions.

Related Topics:
Exponential - Poisson

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An example

An experiment yields the following data: 34,27,45,55,22,34

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To get the arithmetic mean

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• How many items? There are 6. Therefore n=6
• What is the sum of all items? It is 217. Therefore Sigma x (Sigma means sum) is 217
• To get the arithmetic mean divide sigma by n, here 217/6=36.1666666667