Geometric Mean of a Statistical List
Important: The stats package has been deprecated. Use the superseding package Statistics instead.
The function geometricmean of the subpackage stats[describe, ...] computes the geometric mean of the given data.
Classes are assumed to be represented by the class mark, for example 10..12 has the value 11. Missing data are ignored.
The geometric mean is a measure of central tendency. For more information about such measures, please see the information about the mean.
The geometric mean of a set of N numbers is the Nth root of the product of those numbers.
The geometric mean is quite often the most appropriate measure of central tendency to use when ratios or rates are involved.
The command with(stats[describe],geometricmean) allows the use of the abbreviated form of this command.
My investments have been earning me 10% the first year and 20% the second year. The ``average'' earning is
R ≔ describegeometricmean⁡1+10100,1+20100;evalf⁡
which is (about)
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.
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
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:
but not with the arithmetic mean
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