This article is about the median used in statistics. For other medians, check Median (disambiguation).
A median is a measure of central tendency used frequently in statistics.
Mean, Median, Mode
Median of a data set
The median of a finite set of real numbers is defined to be such that . This turns out to be when is odd. When is even, all points between and are medians. If we have to specify one median we conventionally take . (Here denotes the order statistic.) For example, the median of the set is 7.
Median of a distribution
Median of a discrete distribution
If is a discrete distribution, whose support is a subset of a countable set , with for all positive integers , the median of is any point lying between and where and . If for some , is defined to be the median of .
Median of a continuous distribution
If is a continuous distribution, whose support is a subset of the real numbers, the median of is defined to be the such that . Clearly, if has a density , this is equivalent to saying .
Find the median of .
2000 AMC 12 Problems/Problem 14
2004 AMC 12A Problems/Problem 10
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