General term for the several definitions of mean value, the sum divided by the count / From Wikipedia, the free encyclopedia

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There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set.

For a data set, the arithmetic mean, also known as "arithmetic average", is a measure of central tendency of a finite set of numbers: specifically, the sum of the values divided by the number of values. The arithmetic mean of a set of numbers x1, x2, ..., xn is typically denoted using an overhead bar, .[note 1] If the data set were based on a series of observations obtained by sampling from a statistical population, the arithmetic mean is the sample mean () to distinguish it from the mean, or expected value, of the underlying distribution, the population mean (denoted or [note 2]).[1]

Outside probability and statistics, a wide range of other notions of mean are often used in geometry and mathematical analysis; examples are given below.