Mean

A mean is a numeric quantity representing the center of a collection of numbers and is intermediate to the extreme values of a set of numbers. There are several kinds of means 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, ..., x_n is typically denoted using an overhead bar, ${\displaystyle {\bar {x}}}$. 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 (${\displaystyle {\bar {x}}}$) to distinguish it from the mean, or expected value, of the underlying distribution, the population mean (denoted ${\displaystyle \mu }$ or ${\displaystyle \mu _{x}}$).

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