# Talk:Geometric mean

WikiProject Statistics (Rated C-class, High-importance)

This article is within the scope of the WikiProject Statistics, a collaborative effort to improve the coverage of statistics on Wikipedia. If you would like to participate, please visit the project page or join the discussion.

C  This article has been rated as C-Class on the quality scale.
High  This article has been rated as High-importance on the importance scale.
WikiProject Mathematics (Rated C-class, Mid-importance)
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
 C Class
 Mid Importance
Field: Probability and statistics
One of the 500 most frequently viewed mathematics articles.

## When to use the geometric mean plagiarism?

Not sure how to note this, but parts of the When to use Geometric means is cribbed without reference from http://www.math.utoronto.ca/mathnet/questionCorner/geomean.html --128.135.213.42 19:03, 27 March 2007 (UTC)

Apparently this section has been removed some time ago. I have just added a new section about applications with a simple example. Ole Laursen (talk) 10:40, 10 October 2009 (UTC)

I've got a couple of issues with the example given.

1. Why would you expect proportional growth in orange production from a single tree? I don't think the growth rate in the number of oranges produced by a given tree is proportional to the number of oranges produced the previous year. Barring a really good reason for this, I'll change the example to something about bacteria or rabbits or something else commonly found in texts and courses on exponential growth.
2. Because you truncate the annual growth rates, you end up getting the wrong number in the end. Starting at 100 and increasing to 300 in 3 years, the geometric mean is the cube root of 3, or 1.44225, not 1.443. Adam Lein (talk) 21:52, 19 January 2011 (UTC)

## Representations for the G-Mean

I think it's easier to understand the geometric mean as an nth root of a product than as a product raised to the power of a reciprocal, so I added an alternative description in the beginning of the article. Should this become the only description present? Rbarreira 17:13, 15 January 2006 (UTC)

Yes, I think that it should so I took the liberty of removing it. The older less standard version read: $\bigg(\prod_{i=1}^n a_i \bigg)^{1/n} = (a_1 \cdot a_2 \dotsb a_n)^{1/n}$

Nice picture, but what happens when $n>2$? Bob.v.R 14:21, 17 April 2006 (UTC)

## Unclear sentence

I have no idea what this sentence means: This geometric interpretation of the mean is very likely what gave it its name. aevea (talk) 15:02, 11 January 2008 (UTC)

DELETED! In addition to not being referenced, I'm pretty sure the name actually came from the arithmetic/geometric distinction that is essentially synonymous with additive/multiplicative (Cf. the difference between an arithmetic sequence and a geometric one -- the nomenclature there is the same as here). Thus, I'm pretty sure what was there was wrong anyways. ILikeThings (talk) 00:23, 14 August 2008

## Alternative definition

The definition that appears to be used in NY State Math B Regents exams textbooks is The geometric mean of two positive numbers $a$ and $b$ is the positive number $x$ for which $\frac{a}{x} = \frac{x}{b}$. Perhaps this formulation of the definition can be added? 24.164.188.164 (talk) 21:55, 22 May 2009 (UTC)

This is a nice definition. It emphasizes that like the normal (arithmetic) mean of two numbers is half-way between them regarding addition (you add something to the small number to get the mean, and add it again to get the large number), the geometric mean of two numbers is half-way between them regarding multiplication (you multiply the small number by something (x in your formula) to get the mean, and multiply it again to get the large number. This makes it easier to understand what the "oranges" example in the text comes from, and perhaps also the explanation about the logarithmic average, and that the word "geometric" in this mean means the same thing as it does in geometric sequence. Nyh (talk) 08:38, 8 March 2010 (UTC)
The problem I see for including this "definition" is that it is a special case of describing the geometric mean of two numbers. If used as an example of this special case, it could be helpful; however, I don't see this as intrinsically necessary for the article. Drbb01 (talk) 17:16, 8 August 2013 (UTC)

## Note #1 incomplete

Note 1 reads, in part, "The geometric mean only applies to positive numbers in order to avoid taking the root of a negative product..." Pedantically, it should read 'taking the positive root...'. I don't know how to change this, since it seems to be in the first section which has no Edit link. I apologize for my ignorance, and appreciate any help with this minor edit. Trelligan (talk) 19:09, 19 October 2009 (UTC)

I think the point the point is rather that one would not know which root to take, positive, negative or complex. For example, if one had two negative numbers, one would probably want a "mean" value to be negative, while if there wsere one positive and one negative, the product would be negative and hence the formal square root would be purely imaginary (which probably isn't a "good" value for a mean). While one could always work with the geometric mean of the absolute values, it is not really a measure of an average/typical value, in a meaningful sense. (On editing the lead section, either use the "edit this page" tab or there is a user option/preference setting which allows an edit link to appear for the lead section.) Melcombe (talk) 09:29, 20 October 2009 (UTC)

## Applications - Benchmark results

This "section" (it's just one short sentence) is extremely ambiguous. It doesn't even explain what its subject is (I had to mouse over the link to realize it was talking about computing benchmarks). It offers no explanation as to why the geometric mean is the "correct" one. It doesn't specify for what types of benchmarks it is the correct one (all of them? or certain types?). For these reasons, I am removing this section. —Preceding unsigned comment added by Borromean-ring (talkcontribs) 00:08, 5 February 2010 (UTC)

## Redirect from "mean proportional"

The geometric mean used to be also known by the term "mean proportional".89.242.136.4 (talk) 15:58, 22 March 2010 (UTC)

[bookmark.htm 1] Cite error: The opening <ref> tag is malformed or has a bad name (see the help page). –—°″′≈≠≤≥±−×÷←→·§218.75.205.11 (talk) 06:23, 27 July 2013 (UTC)[1]

## Reference Problem

I found that that the link http://hdr.undp.org/en/faq-page is no longer acessible and also I am not sure why the UNDP would be involved in explaining Geometric Mean

## Illustration is baffling

I find the graphs at the top of the article to be useless. It's not clear what the color shading represents or what is the concept illustrated by these four charts? Mheberger (talk) 17:20, 4 September 2014 (UTC)

Seconded and I rm'ed it. Perhaps someone can think of a plot of illustration that adds to the article, but this one was not doing it. a13ean (talk) 18:20, 4 September 2014 (UTC)

Cite error: There are <ref group=bookmark.htm> tags on this page, but the references will not show without a {{reflist|group=bookmark.htm}} template (see the help page).

1. ^ {{[[[[[Category:#REDIRECT [[
<blockquote><ref name="{{#tag:ref|{{Reflist}}<references /><includeonly><noinclude>{{DEFAULTSORT:<!-- <span class="plainlinks"></span> -->}}</noinclude></includeonly>|group="nb"|name=""}}" /></blockquote>

]]]]]]]}}