Very nice wiki article on the subject, one of three Pythagorean means.
The overview of the applications is interesting. Things like: ...
Labor compensation: The geometric mean of a subsistence wage and market value of the labor using capital of employer was suggested as the natural wage by Johann von Thünen in 1875.[16]
What is it about the geometric of the geometric mean making it so appropriate?
https://en.wikipedia.org/wiki/Geometric_mean
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On Wednesday, November 22, 2023 at 11:39:58 AM UTC-8, Fred Bloggs wrote:
Very nice wiki article on the subject, one of three Pythagorean means.
The overview of the applications is interesting. Things like: ...
Labor compensation: The geometric mean of a subsistence wage and market value of the labor using capital of employer was suggested as the natural wage by Johann von Thünen in 1875.[16]
What is it about the geometric of the geometric mean making it so appropriate?
https://en.wikipedia.org/wiki/Geometric_meanYeah, once, on jury duty doing a compensation calculation, I noted that
the square root of the product of the plaintiff's and defendant's suggested numbers was very close to what our tabulation yielded.
After being laughed off, one of the other jurors (a professional at accounting)
made the same observation, using percentage scaling figures...
So, there's a lot of geometric mean applications, and I wonder if the defendant's lawyer
expected X and low-balled by a percentage while the plaintiff's lawyer expected X and
high-balled by the same percentage. Who knows? Not me.
Very nice wiki article on the subject, one of three Pythagorean means.growth rate (CAGR). The geometric mean of growth over periods yields the equivalent constant growth rate that would yield the same final amount.
The overview of the applications is interesting. Things like:
The geometric mean is more appropriate than the arithmetic mean for describing proportional growth, both exponential growth (constant proportional growth) and varying growth; in business the geometric mean of growth rates is known as the compound annual
The geometric mean has from time to time been used to calculate financial indices (the averaging is over the components of the index). For example, in the past the FT 30 index used a geometric mean.[8] It is also used in the CPI calculation[9] andrecently introduced "RPIJ" measure of inflation in the United Kingdom and in the European Union.
Although the geometric mean has been relatively rare in computing social statistics, starting from 2010 the United Nations Human Development Index did switch to this mode of calculation, on the grounds that it better reflected the non-substitutablenature of the statistics being compiled and compared:
The geometric mean decreases the level of substitutability between dimensions [being compared] and at the same time ensures that a 1 percent decline in say life expectancy at birth has the same impact on the HDI as a 1 percent decline in education orincome. Thus, as a basis for comparisons of achievements, this method is also more respectful of the intrinsic differences across the dimensions than a simple average.[10]
Distance to the horizon of a sphere (ignoring the effect of atmospheric refraction when atmosphere is present) is equal to the geometric mean of the distance to the closest point of the sphere and the distance to the farthest point of the sphere.15]
The geometric mean has been used in choosing a compromise aspect ratio in film and video: given two aspect ratios, the geometric mean of them provides a compromise between them, distorting or cropping both in some sense equally.
The geometric mean is also used to calculate B and C series paper formats.
More:
Spectral flatness: in signal processing, spectral flatness, a measure of how flat or spiky a spectrum is, is defined as the ratio of the geometric mean of the power spectrum to its arithmetic mean.
Anti-reflective coatings: In optical coatings, where reflection needs to be minimised between two media of refractive indices n0 and n2, the optimum refractive index n1 of the anti-reflective coating is given by the geometric mean:
?
1
=
?
0
?
2
n_{1}={\sqrt {n_{0}n_{2}}}.
Subtractive color mixing: The spectral reflectance curve for paint mixtures (of equal tinting strength, opacity and dilution) is approximately the geometric mean of the paints' individual reflectance curves computed at each wavelength of their spectra.[
Image processing: The geometric mean filter is used as a noise filter in image processing.
Labor compensation: The geometric mean of a subsistence wage and market value of the labor using capital of employer was suggested as the natural wage by Johann von Thünen in 1875.[16]
What is it about the geometric of the geometric mean making it so appropriate?
https://en.wikipedia.org/wiki/Geometric_mean
On Wed, 22 Nov 2023 11:39:51 -0800 (PST), Fred Bloggs <bloggs.fred...@gmail.com> wrote:annual growth rate (CAGR). The geometric mean of growth over periods yields the equivalent constant growth rate that would yield the same final amount.
Very nice wiki article on the subject, one of three Pythagorean means.
The overview of the applications is interesting. Things like:
The geometric mean is more appropriate than the arithmetic mean for describing proportional growth, both exponential growth (constant proportional growth) and varying growth; in business the geometric mean of growth rates is known as the compound
recently introduced "RPIJ" measure of inflation in the United Kingdom and in the European Union.The geometric mean has from time to time been used to calculate financial indices (the averaging is over the components of the index). For example, in the past the FT 30 index used a geometric mean.[8] It is also used in the CPI calculation[9] and
nature of the statistics being compiled and compared:Although the geometric mean has been relatively rare in computing social statistics, starting from 2010 the United Nations Human Development Index did switch to this mode of calculation, on the grounds that it better reflected the non-substitutable
income. Thus, as a basis for comparisons of achievements, this method is also more respectful of the intrinsic differences across the dimensions than a simple average.[10]The geometric mean decreases the level of substitutability between dimensions [being compared] and at the same time ensures that a 1 percent decline in say life expectancy at birth has the same impact on the HDI as a 1 percent decline in education or
[15]Distance to the horizon of a sphere (ignoring the effect of atmospheric refraction when atmosphere is present) is equal to the geometric mean of the distance to the closest point of the sphere and the distance to the farthest point of the sphere.
The geometric mean has been used in choosing a compromise aspect ratio in film and video: given two aspect ratios, the geometric mean of them provides a compromise between them, distorting or cropping both in some sense equally.
The geometric mean is also used to calculate B and C series paper formats.
More:
Spectral flatness: in signal processing, spectral flatness, a measure of how flat or spiky a spectrum is, is defined as the ratio of the geometric mean of the power spectrum to its arithmetic mean.
Anti-reflective coatings: In optical coatings, where reflection needs to be minimised between two media of refractive indices n0 and n2, the optimum refractive index n1 of the anti-reflective coating is given by the geometric mean:
?
1
=
?
0
?
2
n_{1}={\sqrt {n_{0}n_{2}}}.
Subtractive color mixing: The spectral reflectance curve for paint mixtures (of equal tinting strength, opacity and dilution) is approximately the geometric mean of the paints' individual reflectance curves computed at each wavelength of their spectra.
Image processing: The geometric mean filter is used as a noise filter in image processing.
Labor compensation: The geometric mean of a subsistence wage and market value of the labor using capital of employer was suggested as the natural wage by Johann von Thünen in 1875.[16]
What is it about the geometric of the geometric mean making it so appropriate?
https://en.wikipedia.org/wiki/Geometric_meanGiven two wild guesses that are far apart, like 4:1 for instance, the
gm is the safest guess. It's only off by 2:1 worst case in either
direction and is probably better.
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Subject: Re: Geometric Mean
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