Editing Median (section)

===Efficiency{{anchor|Efficiency}}===

The [[Efficiency (statistics)|efficiency]] of the sample median, measured as the ratio of the variance of the mean to the variance of the median, depends on the sample size and on the underlying population distribution. For a sample of size <math>N = 2n + 1</math> from the [[normal distribution]], the efficiency for large N is

<math display="block"> \frac{2}{\pi} \frac{N+2}{N} </math>

The efficiency tends to <math> \frac{2}{\pi} </math> as <math>N</math> tends to infinity.

In other words, the relative variance of the median will be <math>\pi/2 \approx 1.57</math>, or 57% greater than the variance of the mean – the relative [[standard error]] of the median will be <math>(\pi/2)^\frac{1}{2} \approx 1.25</math>, or 25% greater than the [[standard error of the mean]], <math>\sigma/\sqrt{n}</math> (see also section [[#Sampling distribution]] above.).<ref>{{Cite book | url=https://books.google.com/books?id=8bMj8m-4RDQC&q=standard%20error%20of%20the%20median&pg=PA104 |title = Data Analysis and Graphics Using R: An Example-Based Approach|isbn = 9781139486675|last1 = Maindonald|first1 = John|last2 = John Braun|first2 = W.|date = 2010-05-06| publisher=Cambridge University Press }}</ref>