Talk:mean

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Multiple Etymologies[edit]

<Jun-Dai 20:17, 3 Jun 2005 (UTC)> 24, before I edit the page back, I want to take a moment to talk about this. Wiktionary:Entry layout explained makes it pretty clear that multiple etymologies are to be handled the way I've done it here. If you have issue with this, then rather than simply undoing my changes, it would be better to discuss changing the policy on Wiktionary talk:Entry layout explained. I recognize that it isn't "official" policy per se, but it's the closest thing we have, and I'm not planning on backing down until our policy is defined otherwise. </Jun-Dai>

You said it yourself, it's not policy, and it does not look good. 24 20:32, 3 Jun 2005 (UTC)
<Jun-Dai 20:37, 3 Jun 2005 (UTC)> Not a good enough answer. I don't appreciate your revisions of my formatting, and it's outside of the convention and the closest thing we have to policy, and you haven't given any substantive reasons for it ("it does not look good" doesn't qualify). Discuss this proto-policy at Wiktionary talk:Entry layout explained if you think you have a good reason for altering the standard. </Jun-Dai>
That page means nothing. "Semi-policy"? Where was the polling for that? 24 20:39, 3 Jun 2005 (UTC)
<Jun-Dai 20:41, 3 Jun 2005 (UTC)> Well, it means more than any explanation you've given. The format is standard for every dictionary I've seen, and I haven't seen any good arguments against using it here. </Jun-Dai>
The formatting by Jun-Dai is the standard way of formatting articles, see corporal, can as well as plenty of others for examples of this formatting. - TheDaveRoss
Well, then I will try to do something like that. I will work on it now. 24 20:47, 3 Jun 2005 (UTC)
<Jun-Dai 20:59, 3 Jun 2005 (UTC)> TheDave, can we stick to the mean (1), mean (2) format please? It's consistent with the Entry layout page as well as forte and sake. It's the format I prefer, anyhow, and I'd like to see some discussion about it before we deviate from it. </Jun-Dai>
If you like, we can keep it, but I have seen it the present way more than 'mean (1)...', if only because the latter repeats information (needlessly in my opinion), whereas numbering the etymologies does not. I am going to work on a 'hrunk' which uses each layout fully and then we can discuss and perhaps vote on what we think is the best and most useful. - TheDaveRoss


I've never come across what is recommended under "homographs" on ELE. I've contributed some words to Category:English irregular plurals and always used "Etymology 1", "Etymology 2", etc. This makes more sense because the reason for branching off into several second-level headings is the existence of different etymologies for one spelling, and because, on a page "word", the two lines ===word (1)=== and ====Etymology==== don't provide more information, just more headers, than </nowiki>===Etymology 1===</nowiki>. Ncik 01:33 04 Jun 2005 (UTC)

on a four day trip kamal drove 340 miles,480 miles,500 miles,and 444 miles. What was his mean daily distance?{utc}

Arithmetic mean is 441 miles per day, obviously.
A slightly harder question is this: "Kamal walks up a hill at a steady 2 miles per hour, then run back down at a steady 6 miles per hour. What is his average speed for the journey? dbfirs 17:44, 15 January 2008 (UTC)

Noun: meanings 3 and 4[edit]

I cannot recall ever having heard the word used in either of these senses. What do they "mean"? Have I missed something? dbfirs 17:44, 15 January 2008 (UTC)

Someone mathematical has overmathematicized (It's in my German DNA.) this entry. Sense 3 is really the geometric mean. There are many, many kinds of means, though the most common meaning is the average or arithmetic mean, which is not clear from the entry. Sense 4 reflects a mathematician's understanding of the range of possibilities but also seems dismissive of popular misuse of this "mathematical" term. The variety of mathematical senses is more of interest to WP than to WT, IMHO. DCDuring 18:25, 15 January 2008 (UTC)
What I said was the harmonic mean makes no sense to me at all. I had misread it previously as well. I'm going to rfv-sense it. DCDuring 18:35, 15 January 2008 (UTC)

Just to clarify what's being referred to here. The current senses are:

  1. The average, the arithmetic mean.
  2. Loosely, an intermediate value or range of values.
  3. (mathematics) Any function of multiple variables that satisfies certain properties and yields a number representative of its arguments.
  4. (mathematics) Either of the two numbers in the middle of a proportion, as 2 and 3 in 1:2=3:6.

Sense 3 is then not the geometric mean only, but any mean (arithmetic mean, geometric mean, harmonic mean, root mean square, etc. See w:mean). Not sure why this sense is WP-worthy and not WT-worthy: it's definitely a sense of mean. The fourth sense, which is in the heading of this section but then not referred to again, is, well, another sense, meaning what it says it does. Is the definition unclear?—msh210 19:02, 15 January 2008 (UTC)

I had thought it might have to do with education in mathematics, but I'd long forgotten what it meant. This now looks pretty good to me. The listing of the numerous types of means in derived terms reminded me of the (much, much worse) entry for the derived terms in time. DCDuring 19:33, 15 January 2008 (UTC)!

Thanks for the clarifications! I have never heard "mean" used as a synonym for "median" but the citations prove that the word is so (confusingly) used. (They do not refer to the harmonic mean which is a single value.) Strangely, I was happy with the generalised mathematical definition (including geometric & harmonic means) which was #1 at 17:44 , but I think the current layout is best for the general reader. dbfirs 23:19, 15 January 2008 (UTC)

Sorry that my blunders added to the confusion. Glad I went to the horse's mouth for the explanation of that math-educational sense. The logic of placing the most-common uses near the top favors the most casual user, as it should. Mathematicians might want to go from general to particular. Linguists often want to go in etymological order. Sometimes that order is the same as from concrete to abstract. DCDuring 23:45, 15 January 2008 (UTC)
After further research -- The use of "mean" to signify one or more middle values is much more widespread (outside the UK and especially in the US) than I had imagined, and it dates back to 1571 in the senses cited by Msh210. Mathematics teachers in England would throw out as being long obsolete any text book containing this usage, but it is evidently common elsewhere. The usage might derive from an extension of the geometric mean where the square of the mean is equal to the product of the extremes, or it might just refer to "middle" (after translations of Euclid). I stand corrected! Incidentally, I have found another dozen meanings for "mean" but I am not going to complicate Wiktionary any further because most of them are rare or obsolete! dbfirs 00:00, 16 January 2008 (UTC)
Don't consider rare, obsolete or technical as disqualifying material from WT. My concern is that the common user find what he needs quickly. I also like it if WT can be a convenient source for the obscure. The obscure should not make the basic too hard to find. At some point there may have to be a means of custom- (bespoke-) tailoring the material to user needs, but for all but a few entries that is a remote concern. We have started moving some citations to separate pages if they don't serve as good usage illustrations. There is a simple wiktionary, too. DCDuring 00:12, 16 January 2008 (UTC)
Moving citations of the more obscure usages to a separate page sounds a good idea, making entries of normal modern usage much clearer for the casual user. I like the idea of customising the display, or perhaps just a "show" link for citations, like that for translations. Then there could be another link for technical usage, and for obscure and obsolete usage. This is not necessary for most entries at present, but is Wiktionary planning to be the ultimate reference dictionary eventually? An example of obscure and long obsolete usage would be "mean" = sexual intercourse! (15th century), but anyone studying literature of that period would have specialist reference books which explained the usage wouldn't they? English was almost a different language then. dbfirs 14:19, 16 January 2008 (UTC)
There are folks who talk about all these possibilities, but it is a fairly distant goal. 15th C is condidered late Middle English, isn't it? Old and Middle English are treated as separate languages (albeit not with their own wiki). That older meaning, which survived into early Modern English should have a home as a Middle English entry I think, on the same page. DCDuring 14:43, 16 January 2008 (UTC)
I'm not a historian of English, so I will leave it to someone else to add obsolete meanings if they can find three citations (I would struggle, especially as the spelling was very variable at that time.) I share your inclusionist philosophy (as well as your fallibilist approach) but in moderation. I think I'll direct my efforts towards adding and clarifying definitions of all words regularly used in the last couple of hundred years for now. Thanks for your guidance. Best wishes. dbfirs 19:28, 16 January 2008 (UTC)

RFV — passed[edit]

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This entry has survived Wiktionary's verification process.

Please do not re-nominate for verification without comprehensive reasons for doing so.


Rfv-sense: (mathematics) Any function of multiple variables that satisfies certain properties and yields a number representative of its arguments. As stated that would be a many-to-one mapping or function. I have never seen or heard mean used in this way. Alternatively, this is a definition whose entire meaning depends of the unstated meaning of "certain". If so, I doubt any reasonable definition can be produced that will not be encyclopedic. Please prove me wrong. DCDuring TALK 16:44, 10 November 2008 (UTC)

I think the definition is decent; all it seems to be missing is "or the result of such a function given specific arguments" (or something like that). It covers the arithmetic mean (which, rightly, is also sense 1), the geometric mean, the harmonic mean, the generalized mean (a.k.a. power mean), the generalized f-mean, and weighted versions of any of these. It's unfortunate that so many of our definitions (especially of place names and taxonomic common-names) need to use "certain", "various", and other hedge words to make clear that they're not comprehensive, but I don't see a better way. As you say, a truly comprehensive definition would be encyclopedic, but that doesn't mean we should ignore the sense entirely. —RuakhTALK 23:47, 10 November 2008 (UTC)
The trouble is it doesn't exclude any function whatsoever as stated. It is like defining a "pie" as an "edible object that meets certain conditions". I don't need the whole recipe, but I need a little more than that. In any event, I would like to see citations that support the "sense" (more non-sense, IMO). I think the exercise would improve or remove the sense. DCDuring TALK 00:27, 11 November 2008 (UTC)
Now cited, but if the word's vagueness offend thee, then by all means, pluck it out. I've always felt we're too laid-back about polysemy in the lexicon. ;-)   O.K., so seriously, how about this:
  1. Any of the arithmetic, geometric, or harmonic mean functions, or a weighted version of one of these, or any other variadic real-valued function considered similar to one of these (weighted or otherwise), or the value of any of these.
Sadly, even then we'd be missing a key sense: it's possible to take the (arithmetic) mean of a function over an interval (it's the definite integral divided by the range), hence the celebrated Mean Value Theorem of differential integral calculus; and this can also be weighted, or changed to a power mean (such as the harmonic mean) or f-mean. (I have to admit, I've never seen the geometric mean of a function over an interval, but since the geometric mean is simply the limit of the power mean as the power goes to 0 from either side, I'm sure it can be done and has been done.)
RuakhTALK 05:10, 11 November 2008 (UTC)
Would it be mean of me to argue (not that I would dream of actually doing so) that the cites are of geometric mean and harmonic mean, etc. or that they illustrate sense 2 and add little meaning thereto? By all means, feel free to reject my arguments. At least the RfV has been a means to the end of improving sense 3. DCDuring TALK 10:06, 11 November 2008 (UTC)
Re: "that the cites are of geometric mean and harmonic mean, etc.": I anticipated that argument, and I can't dismiss it out of hand, but I chose quotations that I think argue against it somewhat. A reader encountering the 1997 cite wouldn't know to look up "weighted mean" (since it's "{{probability-weighted} mean}"); a reader encountering the 2002 cite wouldn't know to look up "geometric mean" (since it's "geometric [] means"); and a reader encountering the 2003 cite could be excused for thinking that the word "mean" itself must have some sort of relevant meaning.
Re: "that they illustrate sense 2 and add little meaning thereto": I'm not familiar with sense 2. I've now tagged it with {{rfv-sense}}; if it really exists, then quotes should help us determine the extent to which it's distinct from sense 3 (if at all).
RuakhTALK 15:37, 11 November 2008 (UTC)
I have cites that illustrate the less precise sense 2. The word is also used in engineering contexts where there is considerable ambiguity about whether there is any actual formula or actual measurements: "mean viscosity". The word "mean" can signify "hand-waving" vagueness. DCDuring TALK 16:19, 11 November 2008 (UTC)
I think it is a mistake (from a mathematical viewpoint) to try to generalise 'mean' to indicate that arithmetic, geometric and harmonic means are somehow definable in a similar way. (Sorry, Ruakh, I missed the point of the power mean. I suspect the formula hides certain differences, however, that may come out as issues of convergence of the series.) On the other hand, the probabalistic generalisation of mean is more obviously an extension of the arithmetic mean, via the integral calculus. I also commend the exploration of citations of general or 'vague' usage. Pingku 16:54, 11 November 2008 (UTC)
Ruakh, your definition hides issues of domain. Firstly in terms of real numbers: The harmonic mean should be restricted to sets of positive numbers, to avoid the problem of division by zero. The geometric mean should be restricted to sets of non-negative numbers, to avoid non-real (and multiple) solutions. The arithmetic mean operates over the real domain and seems naturally to generalise to complex numbers. I expect it can be applied to any field.
Wolfram Mathworld has a citeable definition of mean as a homogeneous function that lies (inclusively) between the minimum and maximum of the set. That doesn't quite fit with my generalisation to the complex field (where max and min are not relevant), but I think there's a workaround to do with a distance function (i.e., the distance between the mean and any element in the set should be no greater than the maximum distance between two elements of the set). The entry homogeneous function might also have to be looked at. Pingku 03:24, 17 November 2008 (UTC)

Sense 3 passed; sense 2 still tagged.msh210 23:47, 10 December 2008 (UTC)

And I think I've now cited sense 2.—msh210 23:52, 10 December 2008 (UTC)

I agree. RFV passed sense 2, thanks. —RuakhTALK 03:32, 31 May 2009 (UTC)


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mean [edit]

Etymology 1: Intermediate step.

I had added this 4 years ago. It is (now ?) in the wrong etymology and is, in any event, redundant to the sense in Ety 3, to the extent that it is not an out-and-out error. I would have simply deleted it, but it's been a long time and has attracted two translations. If I was wrong them, it's only a bit less likely that I'm wrong now. The citations support the sense in Ety 3 at least as well as this sense. DCDuring TALK 17:54, 19 September 2012 (UTC)

So, it's correct but under the wrong etymology, and under the correct etymology we already have it, right? Why not move the translations then speedy delete it? Mglovesfun (talk) 08:27, 21 September 2012 (UTC)
Because I might be wrong about this. Are you sure? DCDuring TALK 13:10, 21 September 2012 (UTC)
My best has been done. The sense may be redundant, the gloss may be wrong, and the cites may not support the sense. DCDuring TALK 13:23, 21 September 2012 (UTC)
I have no idea. Mglovesfun (talk) 16:08, 21 September 2012 (UTC)