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===Medians of particular distributions=== The medians of certain types of distributions can be easily calculated from their parameters; furthermore, they exist even for some distributions lacking a well-defined mean, such as the [[Cauchy distribution]]: * The median of a symmetric [[unimodal distribution]] coincides with the mode. * The median of a [[symmetric distribution]] which possesses a mean ''μ'' also takes the value ''μ''. ** The median of a [[normal distribution]] with mean ''μ'' and variance ''σ''<sup>2</sup> is μ. In fact, for a normal distribution, mean = median = mode. ** The median of a [[uniform distribution (continuous)|uniform distribution]] in the interval [''a'', ''b''] is (''a'' + ''b'') / 2, which is also the mean. * The median of a [[Cauchy distribution]] with location parameter ''x''<sub>0</sub> and scale parameter ''y'' is ''x''<sub>0</sub>, the location parameter. * The median of a [[Power law|power law distribution]] ''x''<sup>−''a''</sup>, with exponent ''a'' > 1 is 2<sup>1/(''a'' − 1)</sup>''x''<sub>min</sub>, where ''x''<sub>min</sub> is the minimum value for which the power law holds<ref>{{cite journal | arxiv=cond-mat/0412004 | doi=10.1080/00107510500052444 | title=Power laws, Pareto distributions and Zipf's law | year=2005 | last1=Newman | first1=M. E. J. | journal=Contemporary Physics | volume=46 | issue=5 | pages=323–351 | bibcode=2005ConPh..46..323N | s2cid=2871747 }}</ref> * The median of an [[exponential distribution]] with [[rate parameter]] ''λ'' is the [[natural logarithm]] of 2 divided by the rate parameter: ''λ''<sup>−1</sup>ln 2. * The median of a [[Weibull distribution]] with shape parameter ''k'' and scale parameter ''λ'' is ''λ''(ln 2)<sup>1/''k''</sup>.
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