Median (statistics)
A median is a measure of central tendency used frequently in statistics.
Contents
[hide]Median of a data set
The median of a finite set of real numbers is defined to be
when
is odd and
when
is even, where
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 said to lie between
and
iff
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
Intermediate
Olympiad
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