describe(deprecated)/geometricmean - Help

stats[describe, geometricmean]

Geometric Mean of a Statistical List

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

Parameters

 data - statistical list

Description

 • 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 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.

Examples

Important: The stats package has been deprecated. Use the superseding package Statistics instead.

 > $\mathrm{with}\left(\mathrm{stats}\right)$
 $\left[{\mathrm{anova}}{,}{\mathrm{describe}}{,}{\mathrm{fit}}{,}{\mathrm{importdata}}{,}{\mathrm{random}}{,}{\mathrm{statevalf}}{,}{\mathrm{statplots}}{,}{\mathrm{transform}}\right]$ (1)

My investments have been earning me 10% the first year and 20% the second year. The average'' earning is

 > $R≔\mathrm{describe}[\mathrm{geometricmean}]\left(\left[1+\frac{10}{100},1+\frac{20}{100}\right]\right);$$\mathrm{evalf}\left(\right)$
 ${R}{:=}\frac{{1}}{{25}}{}\sqrt{{33}}{}\sqrt{{25}}$
 $\left[{\mathrm{anova}}{,}{\mathrm{describe}}{,}{\mathrm{fit}}{,}{\mathrm{importdata}}{,}{\mathrm{random}}{,}{\mathrm{statevalf}}{,}{\mathrm{statplots}}{,}{\mathrm{transform}}\right]$ (2)

 > $\mathrm{evalf}\left(100\left(R-1\right)\right)$
 ${14.8912530}$ (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.

 > $1RR;$$\mathrm{evalf}\left(\right)$
 $\frac{{33}}{{25}}$
 ${14.8912530}$ (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

 > $\mathrm{describe}[\mathrm{geometricmean}]\left(\left[3,4\right]\right)$
 $\sqrt{{12}}$ (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:

 > $\frac{1}{\mathrm{describe}[\mathrm{geometricmean}]\left(\left[\frac{1}{3},\frac{1}{4}\right]\right)}$
 $\sqrt{{12}}$ (6)

but not with the arithmetic mean

 > $\mathrm{describe}[\mathrm{mean}]\left(\left[3,4\right]\right)$
 $\frac{{7}}{{2}}$ (7)

versus

 > $\frac{1}{\mathrm{describe}[\mathrm{mean}]\left(\left[\frac{1}{3},\frac{1}{4}\right]\right)}$
 $\frac{{24}}{{7}}$ (8)