Editing Average absolute deviation (section)

== Minimization ==
The measures of statistical dispersion derived from absolute deviation characterize various measures of central tendency as ''minimizing'' dispersion:
The median is the measure of central tendency most associated with the absolute deviation. Some location parameters can be compared as follows:
* [[L2 norm|''L''<sup>2</sup> norm]] statistics: the mean minimizes the [[mean squared error]]
* [[L1 norm|''L''<sup>1</sup> norm]] statistics: the median minimizes ''average'' absolute deviation,
* [[Uniform norm|''L''<sup>∞</sup> norm]] statistics: the [[mid-range]] minimizes the ''maximum'' absolute deviation
* trimmed [[Uniform norm|''L''<sup>∞</sup> norm]] statistics: for example, the [[midhinge]] (average of first and third [[quartile]]s) which minimizes the ''median'' absolute deviation of the whole distribution, also minimizes the ''maximum'' absolute deviation of the distribution after the top and bottom 25% have been trimmed off.