Editing Median (section)

==Finite set of numbers==
The median of a finite list of numbers is the "middle" number, when those numbers are listed in order from smallest to greatest.

If the data set has an odd number of observations, the middle one is selected (after arranging in ascending order). For example, the following list of seven numbers,
{{block indent | em = 1.5 | text = 1, 3, 3, '''6''', 7, 8, 9}}
has the median of ''6'', which is the fourth value.

If the data set has an even number of observations, there is no distinct middle value and the median is usually defined to be the [[arithmetic mean]] of the two middle values.<ref name="StatisticalMedian">{{MathWorld |urlname=StatisticalMedian |title=Statistical Median }}</ref><ref>Simon, Laura J.; [http://www.stat.psu.edu/old_resources/ClassNotes/ljs_07/sld008.htm "Descriptive statistics"] {{webarchive|url=https://web.archive.org/web/20100730032416/http://www.stat.psu.edu/old_resources/ClassNotes/ljs_07/sld008.htm |date=2010-07-30 }}, ''Statistical Education Resource Kit'', Pennsylvania State Department of Statistics</ref> For example, this data set of 8 numbers
{{block indent | em = 1.5 | text = 1, 2, 3, '''4, 5''', 6, 8, 9}}
has a median value of ''4.5'', that is <math>(4 + 5)/2</math>. (In more technical terms, this interprets the median as the fully [[trimmed estimator|trimmed]] [[mid-range]]).  

In general, with this convention, the median can be defined as follows: For a data set <math>x</math> of <math>n</math> elements, ordered from smallest to greatest,

{{block indent | em = 1.5 | text = if <math>n</math> is odd, <math>\operatorname{med}(x) = x_{(n + 1)/ 2} </math>}}
{{block indent | em = 1.5 | text = if <math>n</math> is even, <math>\operatorname{med}(x) = \frac{x_{(n/2)} + x_{((n/2)+1)}}{2} </math>}}

{| class="wikitable"
|+ Comparison of common [[average]]s of values [ 1, 2, 2, 3, 4, 7, 9 ]
! Type
! Description
! Example
! Result
|-
| align="center" | [[Mid-range|Midrange]]
| Midway point between the minimum and the maximum of a data set
| align="center" | '''1''', 2, 2, 3, 4, 7, '''9'''
| align="center" | '''5'''
|-
| align="center" | [[Arithmetic mean]]
| Sum of values of a data set divided by number of values: <math display="inline">\bar{x} = \frac{1}{n} \sum_{i=1}^n x_i</math>
| align="center" | {{nowrap|(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'''
|}