Median
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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.
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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 
.
Problems
Pre-introductory
Find the median of 
.
Introductory
2000 AMC 12 Problems/Problem 14
2004 AMC 12A Problems/Problem 10
Intermediate
Olympiad
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