Talk:Generalized mean

message: This article is about 95% about power means, with an assertion that some people call them "generalized means" (certainly true, but it is clear from below that there are many other things called generalized means).  About 5% of the article is about a link to generalized f-means, but they have their own article.
I propose:
* Generalized mean should be a disambiguation page, with pointers to power mean, Lehmer mean, and f means.  Also rational mean, if that's a real thing (the link doesn't seem to work). 
* This page should be called power mean; it can be rewritten slightly to fit
JoDu987 (talk) 15:28, 20 April 2012 (UTC)
replies: text: Your results are off. If you Google for "power mean" and "generalized mean" in quotes, then you only get 11,800 and 8,370 results, respectively; however, many sites use the phrase "power mean" in unrelated ways ("Does political power mean economic power?"), driving up the former. (I'm sure a few sites also use "generalized mean" in unrelated ways, but it seems much more commonly the case for "power mean.") My best guess is that "power mean" is only somewhat more popular than "generalized mean," and the current presence of generalized f-means in this article makes me loath to move it wholesale to power mean without a stronger reason. Ruakh 21:31, 30 Apr 2005 (UTC)
replies: text: In that case, shouldn't this page be named "generalised mean" with an 's', to parallel the spelling of generalised f-mean (which is apparently the victor after multiple changes)? I don't know the WP rules for US vs. UK spelling, but I assume you want consistency between closely-related articles. 63.150.32.42 01:29, 19 April 2006 (UTC)
thread_title:  Name and structure 

message: It appears that this article should be renamed to Power mean and have Generalized mean redirect to Power mean instead of having Power mean be a redirect for Generalized mean.  Google show 34 million results for power mean and only 3.3 million results for generalized mean.  Furthermore, many of the latter results are "mirrors" of the wikipedia article.--b4hand 15:17, 30 Apr 2005 (UTC)
replies: text: Your results are off. If you Google for "power mean" and "generalized mean" in quotes, then you only get 11,800 and 8,370 results, respectively; however, many sites use the phrase "power mean" in unrelated ways ("Does political power mean economic power?"), driving up the former. (I'm sure a few sites also use "generalized mean" in unrelated ways, but it seems much more commonly the case for "power mean.") My best guess is that "power mean" is only somewhat more popular than "generalized mean," and the current presence of generalized f-means in this article makes me loath to move it wholesale to power mean without a stronger reason. Ruakh 21:31, 30 Apr 2005 (UTC)
replies: text: In that case, shouldn't this page be named "generalised mean" with an 's', to parallel the spelling of generalised f-mean (which is apparently the victor after multiple changes)? I don't know the WP rules for US vs. UK spelling, but I assume you want consistency between closely-related articles. 63.150.32.42 01:29, 19 April 2006 (UTC)
thread_title:  Earlier top comments 

message: The use of the name "Generalized Mean" in this case is absolutely incorrect, the true "Generalized Mean" that certainly embraces ALL the MEANS (Arithmetic, Harmonic, golden, geometric, arithmonic, Power Mean, etc.) is the  Rational Mean.
201.249.205.33 00:25, 27 December 2006 (UTC)
replies: text: it's all a matter of convention. you can always generalize further (while it doesn't neccesarily make sense).  —Preceding unsigned comment added by 78.8.67.67 (talk) 19:39, 14 February 2010 (UTC)
thread_title: Incorrectly using the name "Generalized Mean" 

message: What about a generalized WEIGHTED mean? It's more general, and all the weighted means are derived from it.
Adar Weidman, January 2007.
* I would expect that the weighted version would divide by the sum of the weights, but it does not. Is the definition, as presented in the article at the moment, correct? -- IbexNu (talk) 22:58, 31 March 2018 (UTC)
thread_title:  Generalized Weighted Mean? 

message: I think this article should be a little less technical. The generalized mean is not such an obscure topic in mathematics that a non-mathematician would never need to look it up. Maybe an introduction with basics would make things easier to understand, and the rest of the article may be kept intact.
Goldencako 03:10, 19 October 2007 (UTC)
thread_title:  Simpler 

message: The concepts of norm and generalized mean I find are very similar with the difference that mean is normalised by sample size, but I am confused as to why one does not mention the other. I known one is stats and the other is vector calculus, but can they be safely interlinked or would that open a can of worms in terminology? --Squidonius (talk) 04:25, 12 November 2010 (UTC)
thread_title:  Mean and norm 

message: The exponent is inverted on the LHS of the second to last equation (after applying f(x)). The (p/q)th root should be taken, not the (q/p)th root.
Blandant (talk) 17:30, 16 June 2011 (UTC)
thread_title:  Typo in "Inequality between any two power means" section 

message: Does anyone know the history of the development of the generalized mean?  — Preceding unsigned comment added by 45.44.78.201 (talk) 17:15, 22 January 2019 (UTC)
thread_title: History

message: It is not clear what 'generalised' means in this context? The first statement is: "In mathematics, generalized means (or power mean or Hölder mean from Otto Hölder) are a family of functions for aggregating sets of numbers."
Will it make any difference if 'generalised' is removed? — Preceding unsigned comment added by 192.38.134.15 (talk • contribs) 08:18, 16 April 2023 (UTC)
replies: text: It is generalised in the sense that it is a more general meaning than the usual, more specific, meaning of "mean". This is a standard meaning of "generalised" in mathematics: a general concept covers a wider range of cases that a related specific concept. JBW (talk) 16:02, 11 June 2023 (UTC)
thread_title:  What is the meaning of 'generalised'?