# Talk:Arithmetic mean

Template:Vital article Template:Maths rating Template:WPStatistics

## Contents

- 1 Untitled
- 2 Suggest 2 possible wiki links and 9 possible backlinks for Arithmetic mean.
- 3 Notation
- 4 Resolution
- 5 'Problems with the mean' section
- 6 Empirical mean
- 7 silly redirect?
- 8 Added the POV tag
- 9 Problem using set notation in the definition?
- 10 Video
- 11 Reason for deletion of referenced sentence
- 12 Technical Tag Added to Article

## Untitled

I removed this:

- (When used as a noun, the word "arithmetic" is pronounced with the accent on the second syllable, but when used in the present sense, as an adjective, the accent is on the
*third*syllable: "arithMETic".)

This just seems inappropriate to me, and even condescending, but if anybody else wants to put it back, feel free.

- I put it back, but at the end.

## Suggest 2 possible wiki links and 9 possible backlinks for Arithmetic mean.

An automated Wikipedia link suggester has some possible wiki link suggestions for the Arithmetic_mean article:

- Can link
**horizontal bar**: ...of a population. We use the name of the variable, X, with a horizontal bar over it as the symbol ("X bar") for a sample mean. Both are... - Can link
**Redmond, Washington**: ...]]s. For instance, reporting the "average" annual income in Redmond, Washington as the arithmetic mean of all annual incomes would yield a ...

Additionally, there are some other articles which may be able to linked to this one (also known as "backlinks"):

- In Cauchy distribution, can backlink
**sample mean**: ...riables, each with a standard Cauchy distribution, then the sample mean (''X''<sub>1</sub> + ... + ''X''<sub>''n''</sub>)/''n'' has... - In Skewness, can backlink
**sample mean**: ...re σ is the sample standard deviation and μ is the sample mean.... - In Lexington, Kentucky, can backlink
**mean average**: ...wspaper: [[Lexington Herald-Leader]] === Climate === The mean average temperature in Lexington is 54.9 °F (13 °C). Annual precipi... - In PILOT, can backlink
**arithmetic mean**: ...:''' Compute and assign numeric value. Example: R:Assign arithmetic mean of #X and #Y to #AM... - In Log-normal distribution, can backlink
**arithmetic mean**: ...e used to estimate confidence intervals akin to the way the arithmetic mean and... - In Anomaly time series, can backlink
**arithmetic mean**: ...cycle of some variable is to be subtracted. Instead of the arithmetic mean, other indicators of [[locality]] may also be used, such as... - In Errors and residuals in statistics, can backlink
**sample mean**: ... :<math>X_1, \dots, X_n\sim N( u,\sigma^2)</math> and the sample mean is a random variable distributed thus:... - In Cochran's theorem, can backlink
**sample mean**: ... and 1 degree of freedom respectively. This shows that the sample mean and sample variance are independent; also... - In Ancillary statistic, can backlink
**sample mean**: ...<math>\overline{X}_n=(X_1+\,\cdots\,+X_n)/n</math> :be the sample mean. The [[random variable]]...

*Notes*: The article text has not been changed in any way; Some of these suggestions may be wrong, some may be right.

*Feedback*: I like it, I hate it, Please don't link to — LinkBot 11:27, 1 Dec 2004 (UTC)

- I took care of them! --ZeroOne 18:39, 1 Dec 2004 (UTC)

- All well and good, but links, or back-links, within Wikipedia should not be a substitute for good, clear descriptions in the article that the average reader can grasp. 208.54.86.231 (talk) 12:25, 13 April 2013 (UTC)

## Notation

Is there any simple (i.e. not summation) way to denote a mean of *a*, *b*, and *c* within an expression? The best I know of is: *average (a,b,c)*, which doesn’t even seem half-decent. Would *µ* or *x̅* be used in place of “'average”? (Should *µ* be italicized in the article?) —Frungi 07:38, 11 February 2006 (UTC)

## Resolution

I have been looking for information on this, but I can't find anything to back it up. I once read another issue w/ arithmetic mean is that you get a false sense of resolution in your measurements. For example, if I am measuring temperature over 10 days and each day I can only measure to the nearest degree (meaning 45 degrees or 46 degrees), then it is possible with a data set of (43, 46, 46, 47, 50, 54, 52, 51, 50, 49) to end up with an average temperature of 48.8, making it seem that I can measure with that level of accuracy, which isn't true. While not a real issue with this case, it can be problematic within the science realm. --ronb 20:33, 7 Feb 2007 (UTC)

## 'Problems with the mean' section

Do you guys think maybe this section is a bit cluttered and could stand a small cleanup? --ronb 20:34, 7 Feb 2007 (UTC)

## Empirical mean

Empirical mean redirects here, but the term is not referenced in this page. Is it just a synonym for "Arithmetic mean"? If so, that should be stated. Hv 13:57, 17 February 2007 (UTC)

- I came to this talk page with exactly the same issue as Hv but 7 months later.—PaulTanenbaum 12:49, 27 September 2007 (UTC)

- See empirical measure for explanation what
*empirical mean*means. (Igny 14:35, 27 September 2007 (UTC))

- See empirical measure for explanation what

An empirical mean is the mean of an empirical distribution, and is therefore the same thing as a sample mean. Michael Hardy (talk) 17:49, 14 October 2009 (UTC)

...for now I've redirectd empirical mean to sample mean and sample covariance. Michael Hardy (talk) 17:55, 14 October 2009 (UTC)

## silly redirect?

i don't think "sample mean" should redirect here... —Preceding unsigned comment added by 65.183.135.40 (talk) 01:59, 18 February 2008 (UTC)

## Added the POV tag

The whole section about calling a numerical average (or arithmetic mean or whatever you want to call it) an "average" being WRONG WRONG BAD is completely POV. Just because you personally don't call it that, doesn't mean it isn't in use. Webster backs me up, and so does dictionary.com, see definition nunber 2 in both. If you want to be a linguistic prescriptivist, keep it out of wikipedia mabye? If it doesn't change in a few days, I guess I'll have a crack at fixing it. Thanks all. 219.78.90.231 (talk) 09:26, 10 March 2008 (UTC)

- You were quite right there. This text was added by in a series of edits on 7–8 December by a user who hasn't made any edits since then. I've altered it to something shorter and more neutral but I'm happy for that to be edited further. I've removed the POV tag. I've also removed the sentence about skewness from the lead of the article as it was distracting and out of place. Qwfp (talk) 10:13, 10 March 2008 (UTC)

## Problem using set notation in the definition?

The article defines the mean in terms of "sample space ". I don't see the motivation for using set notation here, and it seems sort of confusing; it tempts one into thinking that maybe a given number cannot be used more than once in calculating the mean, e.g. that if you were taking the mean of numbers 2,2,3,3,5, maybe it would be something like or , rather than . Can someone clarify whether this set notation (and the reference to sample spaces) really helps here? --75.165.90.180 (talk) 16:11, 15 September 2010 (UTC)

## Video

I inserted a video from Khan Academy via the External Media template near the top of the article. This is something of an experiment and please do send me feedback. The idea of the external media template is that we can include media that is copyrighted - so we can't store it on Commons or Wikipedia - but which we would otherwise want to include in the article. Please look at the video and answer two questions 1) is it from a reliable source? and 2) if this material was public domain, would I want to include it in the article? I think the answer here is yes and yes, so we can include the video via the external media template placed where we would include the video if it were public domain. This type of usage is specifically allowed under WP:EL. I'd personally add another question, "Is it commercial"? but this is not required by WP:EL. In any case the Khan Academy is completely non-profit and they give away this video to anybody and everybody online.

I've placed similar external media templates in many art history articles - also from Khan Academy. Some folks think I must be working for KA - which is absolutely not the case. And one or two others must think that placing these videos in the article will completely break down the separation of ordinary "External Links" and the article - but I think the rules at WP:EL will prevent this.

So other than basic feedback, I've got just one question "Where do you think the video best fits in the article?"

Smallbones_{(smalltalk)} 14:06, 11 March 2013 (UTC)

## Reason for deletion of referenced sentence

I'm deleting the last sentence of the section "Problems", which says

*Where a phenomenon is rare in general (for example, emergency room visits among the general population), but occurs frequently in some people (for example, daredevils), then the mean value may be much lower than the median.[2]*

The citation is to an offline textbook which I don't have access to. I believe the quoted passage is incorrect. If the phenomenon is rare, but some people have large values of it (e.g. number of emergency room visits) then for most people (observations) the value will be zero so the median will be zero; hence the mean will be much *higher* than the median. Duoduoduo (talk) 16:19, 25 March 2013 (UTC)

## Technical Tag Added to Article

The article doesn't fully explain it's key terms in a way that the average reader can understand. Instead it over-relies on Wiki-links to definitions in other articles, which makes reading this article too much of a chore for the lay reader. The descriptions that do remain in this article are often vague, incomplete or oblique (describing indirectly rather than directly in plain English). 208.54.86.231 (talk) 12:20, 13 April 2013 (UTC)