Average

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In mathematics, an average, or central tendency[1] of a data set is a measure of the "middle" value of the data set.

There are many different descriptive statistics that can be chosen as a measurement of the central tendency of the data items. These include arithmetic mean, the median and the mode. Other statistical measures such as the standard deviation and the range are called measures of spread and describe how spread out the data is.

An average is a single value that is meant to typify a list of values. If all the numbers in the list are the same, then this number should be used. If the numbers are not the same, an easy way to get a representative value from a list is to randomly pick any number from the list. In the latter case, the average is calculated by combining the values from the set in a specific way and computing a single number as being the average of the set.

The most common method is the arithmetic mean but there are many other types of central tendency, such as median (which is used most often when the distribution of the values is skewed with some small numbers of very high values, as seen with house prices or incomes).[2]

Contents


Calculation

Arithmetic mean

If n numbers are given, each number denoted by ai, where i = 1, ..., n, the arithmetic mean is the [sum] of the ai's divided by n or

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