Difference between revisions of "Median"
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A '''median''' is a measure of central tendency used frequently in statistics. | A '''median''' is a measure of central tendency used frequently in statistics. | ||
+ | ==Mean, Median, Mode== | ||
+ | https://youtu.be/TkZvMa30Juo?t=1504 | ||
== Median of a data set == | == Median of a data set == | ||
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===Introductory=== | ===Introductory=== | ||
[[2000 AMC 12 Problems/Problem 14]] | [[2000 AMC 12 Problems/Problem 14]] | ||
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+ | [[2004 AMC 12A Problems/Problem 10]] | ||
===Intermediate=== | ===Intermediate=== | ||
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{{problems}} | {{problems}} | ||
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+ | == See Also == | ||
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+ | * [[Mean of a set]] | ||
+ | |||
+ | * [[Mode of a set]] |
Latest revision as of 14:30, 12 November 2023
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
[hide]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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