In mathematics and statistics, the arithmetic mean (pronunciation: / /), or simply the mean or average when the context is clear, is the sum of a collection of numbers divided by the number of numbers in the collection. The collection is often a set of results of an experiment, or a set of results from a survey. The term "arithmetic mean" is preferred in some contexts in mathematics and statistics because it helps distinguish it from other means such as the geometric mean and the harmonic mean.
In addition to mathematics and statistics, the arithmetic mean is used frequently in fields such as economics, sociology, and history, and it is used in almost every academic field to some extent. For example, per capita income is the arithmetic average income of a nation's population.
In statistics, a central tendency (or, more commonly, a measure of central tendency) is a central value or a typical value for a probability distribution. It is occasionally called an average or just the center of the distribution. The most common measures of central tendency are the arithmetic mean, the median and the mode. A central tendency can be calculated for either a finite set of values or for a theoretical distribution, such as the normal distribution. Occasionally authors use central tendency (or centrality), to mean "the tendency of quantitative data to cluster around some central value,". This meaning might be expected from the usual dictionary definitions of the words tendency and centrality. Those authors may judge whether data has a strong or a weak central tendency based on the statistical dispersion, as measured by the standard deviation or something similar.
The term "central tendency" dates from the late 1920s.