Editing Talk:Average (section)

== Merge proposal ==

I propose that we merge '''[[central tendency]]''' into '''[[average]]'''.  —[[User:Quantling|<span class="texhtml"><i>Q</i></span>uantling]]&nbsp;([[User talk:Quantling|talk]]&nbsp;&#124;&nbsp;[[Special:Contributions/Quantling|contribs]]) 20:52, 9 February 2026 (UTC)
*'''Merge''' - Both these pages discuss the various alternatives to [[arithmetic mean]] that migh be meant by '''average''' or '''central tendency'''.  There is a tremendous amount of overlap between the two.  —[[User:Quantling|<span class="texhtml"><i>Q</i></span>uantling]]&nbsp;([[User talk:Quantling|talk]]&nbsp;&#124;&nbsp;[[Special:Contributions/Quantling|contribs]]) 20:52, 9 February 2026 (UTC)
*:'''Merge''':
*:Makes sense to me. There's a lot of overlap with '''[[mean]]''' too, and merges with both have been proposed in the past. This would also be a good opportunity to clean up and reorganize some things.
*:What do you think of the following phrasing and structure?
*::{{About|the [[summary statistics|summary statistic]] for location|the graph theory metric|centrality|other uses of the word "center"|center|the Canadian artist|Joe Average|the trait of being cruel|meanness|other uses of the word "mean"|mean (disambiguation)}}
*::{{For|the similar concepts in geometry, graph theory, and politics|centre (geometry)|graph center|centrism}}
*::{{For|the primary specific meaning of the words "mean" and "average" |arithmetic mean}}
*::{{xt|In [[mathematics]], particularly [[statistics]], a '''central value''', a '''mean''', or an '''average''' of a collection or a [[probability distribution]] is an actual or hypothetical member in the middle of it that [[summary statistics|summarizes]] it by representing its overall position. (The word "'''average'''" is also used outside of mathematics to mean common, typical, or normal.) A "'''(measure of) central tendency'''" may refer either to a central value, or to how close the data is to that central value (i.e. [[statistical dispersion]]).}}
*::{{xt|The phrases "'''the average'''" and "'''the mean'''" almost always refer specifically to the [[arithmetic mean]] (or for a probability distribution, [[expected value]]), though other meanings are occasionally used depending on the context. For example, in [[education]], "average" sometimes refers to "the three Ms" of (arithmetic) mean, [[median]], and [[mode]]; additionally, the [[harmonic mean]] is implied in many situations involving [[rate (mathematics)|rates]] or [[ratio]]s.}}
*::{{xt|1=In statistics, the [[sample mean and covariance|sample (arithmetic) mean]] is denoted using an [[overline]] (e.g. <math>\bar{x}</math>, pronounced "x bar", equals <math>\frac{1}{n} \sum_{i=1}^n x_i</math>), and the [[statistical population#Mean|population mean]] is denoted with the Greek letter [[mu (letter)|mu]] (<math>\mu</math>, pronounced /'mjuː/).}}
*::{{xt|'''Properties''' ...}} (with content from {{slink|Average#General_properties}})
*::{{xt|'''Types''' ...}} (with content from {{slink|Average#Statistical_location|Summary_of_types|Miscellaneous_types}}; {{slink|Central_tendency#Measures|Solutions_to_variational_problems}}; {{slink|Mean#Types_of_means|Other_means}})
*:::{{xt|'''Arithmetic mean''' ...}} (with content from {{slink|Mean#Mean_of_a_probability_distribution|Mean_of_a_function}})
*:::{{xt|'''Quasi-arithmetic means''' ... [table with columns "Name", "<math>f</math>", "<math>f^{-1}</math>", "Formula", "Optimization problem"]}} (with content from {{slink|Average#Pythagorean_means}}; {{slink|Mean#Pythagorean_means|Generalized_means|Mean_of_angles_and_cyclical_quantities|Fréchet_mean}})
*:::{{xt|'''Other central values''' [table with columns "Name", "Formula or description", "Optimization problem"]}}
*:::{{xt|'''Variants'''}} (these are listed separately because they can be applied to any kind of mean)
*::::{{xt|'''Weighted mean''' ...}} (with content from {{slink|Mean#Weighted_arithmetic_mean}})
*::::{{xt|'''Winsorized mean''' ...}}
*::::{{xt|'''Truncated mean''' ...}} (with content from {{slink|Mean#Truncated_mean|Interquartile_mean}})
*::::{{xt|'''Moving average''' ...}} (with content from {{slink|Average#Moving_average}})
*::{{xt|'''Relationships''' ...}} (with content from {{slink|Average#Pythagorean_means}}; {{slink|Central_tendency#Relationships_between_the_mean,_median_and_mode}}; {{slink|Mean#Relationship_between_AM,_GM,_and_HM}})
*::{{xt|'''Applications''' ...}} (with content from {{slink|Average#Definitions|Average_percentage_return_and_CAGR}}; {{slink|Mean#Statistical_location|Mean_of_angles_and_cyclical_quantities|Swanson's_rule}})
*::{{xt|'''History''' ...}} (with content from {{slink|Average#History}}; lead of [[Central tendency]])
*::{{xt|'''Limitations''' ...}} (with content from {{slink|Average#Averages_as_a_rhetorical_tool}})
*::Standard footer sections: "See also", "Notes", "References", "Further reading", "External links"
*:[[User:Sollyucko|Solomon Ucko]] ([[User talk:Sollyucko|talk]]) 00:27, 10 February 2026 (UTC)