stats[describe, geometricmean]  Geometric Mean of a Statistical List

Calling Sequence


stats[describe, geometricmean](data)
describe[geometricmean](data)


Description


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The function geometricmean of the subpackage stats[describe, ...] computes the geometric mean of the given data.

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Classes are assumed to be represented by the class mark, for example 10..12 has the value 11. Missing data are ignored.

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The geometric mean is a measure of central tendency. For more information about such measures, please see the information about the mean.

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The geometric mean of a set of N numbers is the Nth root of the product of those numbers.

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The geometric mean is quite often the most appropriate measure of central tendency to use when ratios or rates are involved.

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The command with(stats[describe],geometricmean) allows the use of the abbreviated form of this command.



Examples


Important: The stats package has been deprecated. Use the superseding package Statistics instead.
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 (1) 
My investments have been earning me 10% the first year and 20% the second year. The ``average'' earning is
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 (2) 
which is (about)
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 (3) 
in percentage.
If I have 1 Glock initially, I have 1.1 Glock after 1 year and 1*(1.1)*(1.2)=1.32 Glocks at the end of the second year.
With the average earning I just computed, I have 1*R Glocks after 1 year and 1*R*R Glocks at the end of the second year.
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 (4) 
which is indeed 1.32
As a second example, consider the ratio of the price of item A to the price of item B. One year the ratio is 3, the following year, the ratio is 4. The average ratio is
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 (5) 
One would expect that a typical number to summarize the ratios A/B to be the reciprocal of the typical number used to summarize the ratios B/A. This is indeed the case with the geometric mean:
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 (6) 
but not with the arithmetic mean
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 (7) 
versus
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 (8) 


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