Editing Arithmetic mean (section)

===Continuous probability distributions===
[[File:Comparison mean median mode.svg|thumb|300px|Comparison of two [[log-normal distribution]]s with equal median, but different [[skewness]], resulting in various means and [[mode (statistics)|mode]]s]]

If a numerical property, and any sample of data from it, can take on any value from a continuous range instead of, for example, just integers, then the [[probability]] of a number falling into some range of possible values can be described by integrating a [[continuous probability distribution]] across this range, even when the naive probability for a sample number taking one certain value from infinitely many is zero. In this context, the analog of a weighted average, in which there are infinitely many possibilities for the precise value of the variable in each range, is called the ''mean of the [[probability distribution]]''. The most widely encountered probability distribution is called the [[normal distribution]]; it has the property that all measures of its central tendency, including not just the mean but also the median mentioned above and the mode (the three Ms<ref name=ThreeMs>{{cite web|url=https://www.visualthesaurus.com/cm/lessons/the-three-ms-of-statistics-mode-median-mean/|title=The Three M's of Statistics: Mode, Median, Mean June 30, 2010|website=www.visualthesaurus.com|author=Thinkmap Visual Thesaurus|date=2010-06-30|access-date=2018-12-03}}</ref>), are equal. This equality does not hold for other probability distributions, as illustrated for the log-normal distribution here.