Median
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.
Contents
Mean, Median, Mode
https://youtu.be/TkZvMa30Juo?t=1504
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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