Editing Average (section)

==Statistical location==
{{See also|Mean#Statistical location}}

The [[Mode (statistics)|mode]], the [[median]], and the [[mid-range]] are often used in addition to the [[mean]] as estimates of central tendency in [[descriptive statistics]]. These can all be seen as minimizing variation by some measure; see {{slink|Central tendency|Solutions to variational problems}}.

{| class="wikitable"
|+ Comparison of common averages of values { 1, 2, 2, 3, 4, 7, 9 }
|-
! Type
! Description
! Example
! Result
|-
| align="center" | [[Arithmetic mean]]
| Sum of values of a data set divided by number of values: <math>\scriptstyle\bar{x} = \frac{1}{n}\sum_{i=1}^n x_i</math>
| align="center" | (1+2+2+3+4+7+9) / 7
| align="center" | '''4'''
|-
| align="center" | [[Median]]
| Middle value separating the greater and lesser halves of a data set
| align="center" | 1, 2, 2, '''3''', 4, 7, 9
| align="center" | '''3'''
|-
| align="center" | [[Mode (statistics)|Mode]]
| Most frequent value in a data set
| align="center" | 1, '''2''', '''2''', 3, 4, 7, 9
| align="center" | '''2'''
|-
| align="center" | [[Mid-range]]
| The arithmetic mean of the highest and lowest values of a set
| align="center" | (1+9) / 2
| align="center" | '''5'''
|}

===Mode===
{{Main|Mode (statistics)}}
[[File:Comparison mean median mode.svg|thumb|upright=1.35|Comparison of [[mean|arithmetic mean]], [[median]] and [[mode (statistics)|mode]] of two [[log-normal distribution]]s with different [[skewness]]]]

The most frequently occurring number in a list is called the mode. For example, the mode of the list (1, 2, 2, 3, 3, 3, 4) is 3. It may happen that there are two or more numbers which occur equally often and more often than any other number. In this case there is no agreed definition of mode. Some authors say they are all modes and some say there is no mode.

===Median===
{{Main|Median}}

The median is the middle number of the group when they are ranked in order. (If there are an even number of numbers, the mean of the middle two is taken.)

Thus to find the median, order the list according to its elements' magnitude and then repeatedly remove the pair consisting of the highest and lowest values until either one or two values are left. If exactly one value is left, it is the median; if two values, the median is the arithmetic mean of these two. This method takes the list 1, 7, 3, 13 and orders it to read 1, 3, 7, 13. Then the 1 and 13 are removed to obtain the list 3, 7. Since there are two elements in this remaining list, the median is their arithmetic mean, (3 + 7)/2 = 5.

===Mid-range===
{{Main|Mid-range}}

The mid-range is the arithmetic mean of the highest and lowest values of a set.