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:''This article is about the statistical method, for alternative meanings see
Median.''
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In
statistics, the '''median''' is that value that separates the highest half of the sample from the lowest half. More precisely 1/2 of the population will have values less than or equal to the ''median'' and 1/2 of the population will have values equal to or greater than the median. To find the ''median'', arrange all the observations from lowest value to highest value and pick the middle one. If there are an even number of observations, take the
mean of the two middle values. When we use the ''median'' to describe what the observations have in common, there are several choices for a measure of variability, the
range, the
interquartile range, and the
absolute deviation. Since the median is the same as the ''second quartile'', its calculation is illustrated in the article on
quartiles.
The median is primarily used for
skewed distributions, which it represents more accurately than the
arithmetic mean. Consider the set {1, 2, 2, 2, 3, 9}. The median is 2 in this case, as is the
mode, and it might be seen as a better indication of
central tendency than the
arithmetic mean of 3.166....
The median is also the central point which minimises the average of the absolute deviations; in the example above this would be (1 + 0 + 0 + 0 + 1 + 7)/6 = 1.5 using the median, while it would be 1.944... using the mean.
Even though
sorting ''n'' items takes in general
O(''n'' log ''n'') operations, by using a
recursive "Divide-and-Conquer" algorithm the median of ''n'' items can be computed with only O(''n'') operations.
Calculation of medians is a popular technique in
summary statistics and
summarizing statistical data, since it is simple to understand and easy to calculate, while also giving a measure that is more robust in the presence of
outlier values than is the
mean. The difference between the median and the mean is less than or equal to one
standard deviation.
==See also==
*
an inequality on location and scale parameters
==See also==
*
Median number
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