Editing Equivariant map (section)

===Statistics===
Another class of simple examples comes from [[statistical estimation]]. The [[mean]] of a sample (a set of real numbers) is commonly used as a [[central tendency]] of the sample. It is equivariant under [[Linear function (calculus)|linear transformation]]s of the real numbers, so for instance it is unaffected by the choice of units used to represent the numbers. By contrast, the mean is not equivariant with respect to nonlinear transformations such as exponentials.

The [[median]] of a sample is equivariant for a much larger group of transformations, the (strictly) [[monotonic function]]s of the real numbers. This analysis indicates that the median is more [[robust statistics|robust]] against certain kinds of changes to a data set, and that (unlike the mean) it is meaningful for [[ordinal data]].<ref>{{citation|title=Measurement theory: Frequently asked questions (Version 3)|date=September 14, 1997|publisher=SAS Institute Inc.|url=http://www.medicine.mcgill.ca/epidemiology/courses/EPIB654/Summer2010/EF/measurement%20scales.pdf|first=Warren S.|last=Sarle}}. Revision of a chapter in ''Disseminations of the International Statistical Applications Institute'' (4th ed.), vol.&nbsp;1, 1995, Wichita: ACG Press, pp. 61–66.</ref>

The concepts of an [[invariant estimator]] and equivariant estimator have been used to formalize this style of analysis.