Talk:Geometric mean

message: 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)
thread_title:  When to use the geometric mean plagiarism?

message: 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)
thread_title:  Representations for the G-Mean

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

message: 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)
replies: text: 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)
replies: text: 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)
thread_title:  Alternative definition 

message: 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)
replies: text: 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)
thread_title:  Note #1 incomplete

message: 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 (talk • contribs) 00:08, 5 February 2010 (UTC)
thread_title:  Applications - Benchmark results 

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

message: 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)
replies: text: 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)
thread_title:  Illustration is baffling 

message: The properties section contains a discussion of why the geometric mean is the appropriate mean for normalized numbers, referring to Flemming and Wallace, 1986. However, this reasoning has been contested by Smith, 1988. I added this reference together with a summary of the paper. Furthermore, these two papers refer to the specific case of averaging computer performance benchmark results, so it is strange that it is in the general Properties section of the Geometric mean article. I would advocate to put this discussion in the Applications section. Seyerman (talk) 10:46, 12 February 2015 (UTC)
replies: text: Because of the notable relationship of the Pythagorean means I looked at how the harmonic means apply in each table and WP:BOLDed it onto the page. It agrees quite strongly with the position advanced by 69.53.236.236 and probably the one by Seyerman. Please compare that to the following table normalized to Computer C, where the arithmetic and geometric both champion Computer C whereas harmonic champions Computer A again. Warmest Regards, :)—thecurran Speak your mind my past 09:20, 6 February 2016 (UTC)
thread_title:  Contested discussion in Properties section 

message: Computer A 	Computer B 	Computer C
Program 1      	0.05       	0.5        	1
Program 2      	50         	5          	1
Arithmetic mean	25.025     	2.75       	1
Geometric mean 	1.581 . . .	1.581 . . .	1
Harmonic mean  	0.099 . . .	0.909 . . .	1
I think academically this case should be present in the page but I'm wary that it might not flow well enough. Warmest Regards, :)—thecurran Speak your mind my past 09:23, 6 February 2016 (UTC)
thread_title:  Shall we add the table as normalized to Computer C? 

message: Scientifically it's far more appropriate to communicate fractional components within a related set of numbers out to a consistent number of significant figures rather than to a consistent number of 'decimal places' hence scientific notation but to maintain the article's original flow, all additional data was truncated after the third 'decimal place'. Please find below all four tables rounded out to a maximum of four significant figures.
          	Computer A	Computer B	Computer C
Program 1      	1         	10        	20
Program 2      	1000      	100       	20
Arithmetic mean	500.5     	55        	20
Geometric mean 	31.62     	31.62     	20
Harmonic mean  	667.1     	70.97     	20
          	Computer A	Computer B	Computer C
Program 1      	1         	10        	20
Program 2      	1         	0.1       	0.02
Arithmetic mean	1         	5.05      	10.01
Geometric mean 	1         	1         	0.6325
Harmonic mean  	1         	0.1980    	0.03996
          	Computer A	Computer B	Computer C
Program 1      	0.1       	1         	2
Program 2      	10        	1         	0.2
Arithmetic mean	5.05      	1         	1.1
Geometric mean 	1         	1         	0.6325
Harmonic mean  	0.1980    	1         	0.3636
          	Computer A	Computer B	Computer C
Program 1      	0.05      	0.5       	1
Program 2      	50        	5         	1
Arithmetic mean	25.025    	2.75      	1
Geometric mean 	1.581     	1.581     	1
Harmonic mean  	0.09990   	0.9091    	1
Opinions? Warmest Regards, :)—thecurran Speak your mind my past 09:45, 6 February 2016 (UTC)
thread_title:  [[Significant figures]] versus decimal places in '''Properties''' computer table? 

message: The first table in the Properties section contains two errors in computing the Harmonic mean.  The table is currently
          	Computer A   	Computer B  	Computer C
Program 1      	1            	10          	20
Program 2      	1000         	100         	20
Arithmetic mean	500.5        	55          	20
Geometric mean 	31.622 . . . 	31.622 . . .	20
Harmonic mean  	667.110 . . .	70.967 . . .	20
But it ought to be
          	Computer A  	Computer B  	Computer C
Program 1      	1           	10          	20
Program 2      	1000        	100         	20
Arithmetic mean	500.5       	55          	20
Geometric mean 	31.622 . . .	31.622 . . .	20
Harmonic mean  	1.998 . . . 	18.182 . . .	20
This changes the validity of the next sentence, ″The arithmetic, geometric, and harmonic means "agree" that computer C is the fastest.″  This affects the entire narrative of the section.
MathatGrace (talk) 19:47, 9 February 2016 (UTC)
replies: text: It appears I'm the second one to notice such a confusing mistake in the table. Just eyeballing it, one can see that it doesn't satisfy the identity HM <= GM <= AM. I'll fix the table now. 68.226.23.184 (talk) 04:13, 18 February 2016 (UTC)
thread_title:  Error in Properties section 

message: The text for the picture currently states, "Geometric mean or mean proportional,[1] in an example with the length l2 is perpendicular to AB."
2 problems:  "with the length 12 is ..." is incorrect grammar, someone should fix that to "in an example with the length l2 perpendicular to AB".
But the reason I don't do this is because the premise of the sentence is incorrect. l2 is a length, it can't be perpendicular to anything. l2's line, BC' is clearly parallel to line AB. BC is perpendicular to AB, and has the length l2, but I don't think this connection is clear just by the description. Someone more knowledgeable in geometry should be able to word this better to let the reader know the significance of the picture... --208.99.251.161 (talk) 13:13, 6 September 2017 (UTC)
replies: text: Thanks for your entry, I hope it is now understandable. Greeting from Munich Petrus3743 (talk) 22:18, 7 September 2017 (UTC)
thread_title:  Example image description ambiguous 

message: The entire article should be rewritten under the assumption that the input numbers are all greater than zero, because it makes more mathematical sense.  Why ever risk taking the n-th root of a negative or zero number?
Daniel R. Grayson (talk) 22:37, 11 May 2018 (UTC)
thread_title:  Should be used only for positive numbers 

message: I was wondering, lets say I have a set of independent random variables, each having own mean and variance, and all of them having standard guassian distribution. Having mean and standard deviation estimations, how do I estimate an error (standard deviation) of the geometric mean? I am not talking about Geometric standard deviation, which is different thing. 2A02:168:F609:0:7855:CA84:B8D8:C659 (talk) 18:57, 11 August 2019 (UTC)
thread_title:  Geometric mean error propagation. 

message: I've tagged a remark in the article as being weasel words, since it suggests using the Bolzano–Weierstrass theorem to prove that the geometric mean is the arithmetic–harmonic mean. While technically true—you could use Bolzano–Weierstrass at a point in such a proof—it is mostly confusing as it glosses over a lot of set-up that would be needed before Bolzano–Weierstrass could be applied. A good argument for showing that the arithmetic–harmonic mean exists is to modify that found in the Arithmetic–geometric mean article.
A minimal improvement would be to instead refer to the Squeeze theorem, since this is more likely to help a reader fill in the missing details, but that still leaves the reader having to demonstrate that a_n - h_n in fact goes to 0 (which a Bolzano–Weierstrass proof would also need). 130.243.94.123 (talk) 17:02, 29 March 2021 (UTC)
thread_title:  Bolzano–Weierstrass weasel 

message: Mean Average, Quatratic and Root mean arr a special cases of Kolmogorov Mean. Sergei Kazariants (talk) 21:44, 16 April 2023 (UTC)
thread_title:  Kolmogorov Mean