# Expectation means average?

We have three ambiguous tags , and . They are often used for and problems. The tag has been synonymized with . The current tag excerpts and info for these three tags are not clear enough.

1. The tag includes arithmetic means and its tag info involves .

In its most general definition, an average is a summary of a set of values. Normally it refers to the arithmetic mean, but other means may be employed (geometric, harmonic, etc.) or a transformation may be applied before and after taking a mean (e.g. root-mean-square).

2. The tag info involves arithmetic means and .

In probability and statistics, mean and expected value are used synonymously to refer to one measure of the central tendency either of a probability distribution or of the random variable characterized by that distribution. For a data set, refers to a central value of a discrete set of numbers: specifically, the sum of the values divided by the number of values. Reference: Wikipedia.

For a finite population, the population mean of a property is equal to the arithmetic mean of the given property while considering every member of the population.

3. The tag info is missing. The "computations" in its tag excerpt give rise to the of ?

For questions about the expectation of a random variable: computations, upper/lower bounds, etc.

Proposal:

1. Synonymize , and as the first sentence in the tag info suggest.
2. Use the tag for non- questions which don't involve .

• I had proposed to synonymize and before I posted this question since the former is a synonym of . However, from the comments under this question, it seems that that doesn't help sorting questions. Unluckily, there's no way to retract this suggestion. Therefore, please downvote this so that it will disappear. It has been deleted thanks to the two users who downvoted this.
• Another proposal is to synonymize with . That's off-topic in this question.
• What specifically do you propose in 1? Do you also want to syn with probabilty or remove that syn and bundle the others together? – quid May 6 '18 at 17:46
• @quid I don't know why (probability) and (expected-value) are syn, but both are possible solutions. I personally prefer the later though. – GNUSupporter 8964民主女神 地下教會 May 6 '18 at 18:07
• I don't understand that synonym either; maybe it made sense when the site was small. – quid May 6 '18 at 18:59
• While we are on the subject of probability tags, let me recall that (conditional-probability) was merged with (probability) some time ago and that this decision was unwise, see the comments there. – Did May 6 '18 at 19:40
• The 734 questions under means are an even mix of questions about expectation of random variables, statistics questions about sample means, and questions about geometric means and the like. I think it gets even more confusing if that particular tag is made a synonym of anything else. – Misha Lavrov May 7 '18 at 1:17
• (I fully support making expected-value its own tag separate from probability and making expectation its synonym, though.) – Misha Lavrov May 7 '18 at 1:18
• Most of the questions tagged means+inequality are about various kinds of means such as AM, GM, QM, HM. Although now there is a separated tag for (a.m.-g.m.-inequality), but this was not always the case.) – Martin Sleziak May 7 '18 at 7:33
• @quid and GNU Supporter - something about the history of the synonym between (expected-value) and (probability) can be found in this answer (and comment below). I have also left a few comments in chat. – Martin Sleziak May 7 '18 at 7:39
• @MishaLavrov I see that there are three senses of this word: 1. Non-probabilistic and non-statistical: Mean Value Theorem, integration of period functions, AM-GM, basic word problem asking for arithmetic mean, etc 2. Probabilistic: expectations of random variables without data collection 3. Statistical: a central tendency estimate after data collection: i.e. sample mean. However, I can't think of words to be used as tag names to distinguish these senses. – GNUSupporter 8964民主女神 地下教會 May 7 '18 at 9:38
• @GNUSupporter I see that you have suggested a synonym (expecation) $\to$ (probability) and now users with sufficient score in (probability) tag can vote on that suggestion. Maybe mentioning this also explicitly in your post could be useful. (At least it could bring more attention of potential voters to the suggested synonym.) – Martin Sleziak May 27 '18 at 19:32
• @MartinSleziak Sorry for late response. I've edited my questions. In fact, I regret this suggestion. Please downvote this. – GNUSupporter 8964民主女神 地下教會 May 30 '18 at 19:14
• @MishaLavrov If you're suggestion is to cancel the synonym (expected-value) $\to$ (probability), maybe you could post this proposal as answer. In this way we could see from voting and comments on that answer what other users think about this suggestion. – Martin Sleziak May 31 '18 at 4:25
• I will point out that the suggestion to synonymize (expectation) $\to$ (probability) is no longer there. (So most likely two users obliged your wishes and downvoted it.) Of course, that does not prevent somebody else from creating the same suggestion again. It probably all depends a bit on the outcome of this discussion. (Personally, I find it a bit unusual that (expectation) and (expected-value) are treated differently.) – Martin Sleziak May 31 '18 at 21:32
• @MartinSleziak Agreed. Thx for update. – GNUSupporter 8964民主女神 地下教會 Jun 1 '18 at 13:51
• I removed the expexted-value synonym. I'll attend to this more fully soon. (I hope. ) – quid Aug 26 '18 at 0:00

I propose that should no longer be a synonym of , and should become a synonym of , which would clear up at least 50% of the confusion here.

(So that voting on this proposal could actually mean something, I will avoid weighing in on here.)

• +1 I support keeping average/mean separate from expectation/expected-value. – GEdgar Jun 2 '18 at 13:48
• I did that. The master tag is now 'expected-value' but it could also be swapped. I did it that way as this is what was proposed. – quid Aug 26 '18 at 0:14

I see a confusion between informal and technical (precise) language. Informally, arithmetic mean is most often referred to as "average". This is not good enough for technical discussions. There are several averages, such as the (arithmetic) mean, median, mode, etc. Expectation is most often associated with the mean, although the two are not identical. Expectation is most basically defined on random variables. The kind of random variable will then result in a specific computation formula, one possibility being the arithmetic mean lookalike.

• Thanks for reply. This is an answer to my question in my title, but the main issue is about the ambiguity of these three tags. I wrote this title so short that it's easy to remember. – GNUSupporter 8964民主女神 地下教會 May 7 '18 at 10:01
• Nevertheless the tag for robust-statistics seems at least relevant to the distinction between average and expectation. – hardmath May 7 '18 at 21:40

As for the issue of tags and ambiguity, I would not lose my sleep over it. The natural languages and formal language, such as in mathematics or logic, have different degrees of fuzziness and ambiguity; for that reason they are not in one to one and onto correspondence with respect to these issues. Just look into any (natural) dictionary. It consists of "tags" (words) right?, but they are so intertwined and overlapping. In many respects, ambiguity in tags is a good thing.

• Ambiguity in tags requires additional care in a search. This can be avoided by more clear tags. Some even abandon these tags, rendering them useless. – GNUSupporter 8964民主女神 地下教會 May 9 '18 at 3:38
• The "small" problem is that ambiguity is unavoidable. My claim is that is is also desirable (alas in a limited amount). – Rado May 9 '18 at 4:50
• Ambiguity in tags is undesirable because those who follow the tags for a certain meaning might not want to care about the other, and it could be considered as "noise". – Andrew T. May 14 '18 at 2:58