Median (Statistics)
Formula and examples for the statistical median (middle value) of a series of numbers
In statistics the median is the value separating the higher half from the lower half of a data series. The median is the middle value of a sorted list.
Example
\(\displaystyle 1, 3,\color{#44F}{\underline{5}},7,9 \)
In the example above, the middle value is 5.
If the number of values is odd, the middle number is the median.
For example with the unordered list
\(7, 9, 12, 1, 3, 2, 14 \)
7 is the median, because this value is in the middle of the ordered list.
\(1, 2, 3, \color{#44F}{\underline{7}}, 9, 12, 14\)
If the number of values is even, the median is defined as the arithmetic mean of the middle two numbers. For example with the unordered list
\( 7, 9, 12, 1, 3, 2, 14, 8\)
the value 7.5 is the median, because the two values 7 and 8 are in the middle of the ordered list.
\(1, 2, 3, \color{#44F}{\underline{7,8}}, 9, 12, 14\)
With the values
\(1,2,6,9\)
the value 4 is the median, because 4 is the mean between the two values 2 and 6.
\(1, \color{#44F}{\underline{2,6}},9\)
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