# Mean

## General term for a numerical value summarizing a group of data / From Wikipedia, the free encyclopedia

#### Dear Wikiwand AI, let's keep it short by simply answering these key questions:

Can you list the top facts and stats about Mean?

Summarize this article for a 10 year old

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.^{[1]} There are several kinds of **means** (or "measures of central tendency") in mathematics, especially in statistics. Each attempts to summarize or typify a given group of data, illustrating the magnitude and sign of the data set. Which of these measures is most illuminating depends on what is being measured, and on context and purpose.

The *arithmetic mean*, also known as "arithmetic average", is the sum of the values divided by the number of values. The arithmetic mean of a set of numbers *x*_{1}, *x*_{2}, ..., x* _{n}* is typically denoted using an overhead bar, ${\bar {x}}$.

^{[note 1]}If the numbers are from observing a sample of a larger group, the arithmetic mean is termed the

*sample mean*(${\bar {x}}$) to distinguish it from the group mean (or expected value) of the underlying distribution, denoted

**$\mu$**or

**$\mu _{x}$**.

^{[note 2]}

^{[2]}

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