Editing Mode (statistics) (section)

===Properties===
Assuming definedness, and for simplicity uniqueness, the following are some of the most interesting properties.
* All three measures have the following property: If the random variable (or each value from the sample) is subjected to the linear or [[affine transformation]], which replaces {{mvar|X}} by {{math|''aX'' + ''b''}}, so are the mean, median and mode.
* Except for extremely small samples, the mode is insensitive to "[[outliers]]" (such as occasional, rare, false experimental readings). The median is also very robust in the presence of outliers, while the mean is rather sensitive.
* In continuous [[unimodal distribution]]s the median often lies between the mean and the mode, about one third of the way going from mean to mode. In a formula, median ≈ (2 × mean + mode)/3. This rule, due to [[Karl Pearson]], often applies to slightly non-symmetric distributions that resemble a normal distribution, but it is not always true and in general the three statistics can appear in any order.<ref>{{cite web |url=http://www.se16.info/hgb/median.htm |title=Relationship between the mean, median, mode, and standard deviation in a unimodal distribution }}</ref><ref>{{cite journal |last=Hippel |first=Paul T. von |year=2005 |url=http://www.amstat.org/publications/jse/v13n2/vonhippel.html |title=Mean, Median, and Skew: Correcting a Textbook Rule |journal=Journal of Statistics Education |volume=13 |issue=2 |doi= 10.1080/10691898.2005.11910556|doi-access=free }}</ref>
* For unimodal distributions, the mode is within {{radic|3}} standard deviations of the mean, and the root mean square deviation about the mode is between the standard deviation and twice the standard deviation.<ref>{{cite journal |last=Bottomley |first=H. |year=2004 |url=http://www.se16.info/hgb/mode.pdf |title=Maximum distance between the mode and the mean of a unimodal distribution |journal=Unpublished Preprint }}</ref>