Editing Arithmetic mean (section)

==Contrast with median==
{{main|Median}}

The arithmetic mean may be contrasted with the [[median]]. The median is defined such that no more than half the values are larger, and no more than half are smaller than it. If elements in the data [[arithmetic progression|increase arithmetically]] when placed in some order, then the median and arithmetic average are equal. For example, consider the data sample <math>\{1,2,3,4\}</math>. The mean is <math>2.5</math>, as is the median. However, when we consider a sample that cannot be arranged to increase arithmetically, such as <math>\{1,2,4,8,16\}</math>, the median and arithmetic average can differ significantly. In this case, the arithmetic average is <math>6.2</math>, while the median is <math>4</math>. The average value can vary considerably from most values in the sample and can be larger or smaller than most.

There are applications of this phenomenon in many fields. For example, since the 1980s, the median income in the United States has increased more slowly than the arithmetic average of income.<ref>{{cite magazine|first=Paul|last=Krugman|url=http://prospect.org/article/rich-right-and-facts-deconstructing-inequality-debate|title=The Rich, the Right, and the Facts: Deconstructing the Income Distribution Debate|magazine=The American Prospect|date=4 June 2014|orig-year=Fall 1992}}</ref>