Mean

A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several kinds of means (or "measures of <a href="/facts/Central_tendency/9yhcQ6me">central tendency</a>") in <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, especially in <a href="/facts/Statistics/DNPsKGYU">statistics</a>. Each attempts to summarize or typify a given group of <a href="/facts/Data/AUBFN97o">data</a>, illustrating the <a href="/facts/Magnitude_(mathematics)/KCn9PoF0">magnitude</a> and <a href="/facts/Sign_(mathematics)/z0xollg1">sign</a> of the <a href="/facts/Data_set/eDvegUTK">data set</a>. Which of these measures is most illuminating depends on what is being measured, and on context and purpose.
The <a href="/facts/Arithmetic_mean/L3Pv333o">arithmetic mean</a>, 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 x1, x2, ..., xn is typically denoted using an <a href="/facts/Overhead_bar/PH46XuIu">overhead bar</a>, 
 
 
 
 
 
 
 x
 ¯
 
 
 
 
 
 {\displaystyle {\bar {x}}}
 
. If the numbers are from observing a <a href="/facts/Sampling_(statistics)/kIb01xdL">sample</a> of a <a href="/facts/Statistical_population/KAILs8E3">larger group</a>, the arithmetic mean is termed the <a href="/facts/Sample_mean/Ah8VVVDT">sample mean</a> (
 
 
 
 
 
 
 x
 ¯
 
 
 
 
 
 {\displaystyle {\bar {x}}}
 
) to distinguish it from the <a href="/facts/Population_mean/swcEd4Pg">group mean</a> (or <a href="/facts/Expected_value/1XV0JKL8">expected value</a>) of the underlying distribution, denoted 
 
 
 
 μ
 
 
 {\displaystyle \mu }
 
 or 
 
 
 
 
 μ
 
 x
 
 
 
 
 {\displaystyle \mu _{x}}
 
.
Outside probability and statistics, a wide range of other notions of mean are often used in <a href="/facts/Geometry/wTQf5ffQ">geometry</a> and <a href="/facts/Mathematical_analysis/XXeR26Ih">mathematical analysis</a>; examples are given below.

Mean open-in-new

Mean