Difference between revisions of "Median (statistics)"
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− | A '''median''' is a | + | A '''median''' is a measure of central tendency used frequently in statistics. |
− | == | + | == Median of a data set == |
− | The median of a [[finite]] [[set]] of [[real number]]s is | + | The median of a [[finite]] [[set]] of [[real number]]s <math>\{X_1, ..., X_k\}</math> is defined to be <math>X_{(\frac{k+1}2)}</math> when <math>k</math> is odd and <math>\frac{X_{(\frac{k}2)} + X_{(\frac{k}2 + 1)}}2</math> when <math>k</math> is even, where <math>X_{(i)}, i \in \{1,...,k\}</math> denotes the <math>k^{th}</math> [[order statistic]]. For example, the median of the set <math>\{2, 3, 5, 7, 11, 13, 17\}</math> is 7. |
− | + | == Median of a distribution == | |
+ | === Median of a discrete distribution === | ||
− | + | If <math>F</math> is a discrete distribution, whose support is a subset of a countable set <math>{x_1, x_2, x_3, ...}</math>, with <math>x_i < x_{i+1}</math> for all positive integers <math>i</math>, the median of <math>F</math> is said to lie between <math>x_i</math> and <math>x_{i+1}</math> iff <math>F(x_i)\leq\frac12</math> and <math>F(x_{i+1})\geq\frac12</math>. If <math>F(x_i)=\frac12</math> for some <math>i</math>, <math>x_i</math> is defiend to be the median of <math>F</math>. | |
== Problems == | == Problems == |
Revision as of 05:54, 25 November 2007
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 defiend to be the median of .
Problems
Pre-introductory
Find the median of .
Introductory
Intermediate
Olympiad
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