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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 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.

Examples

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

withstats

anova,describe,fit,importdata,random,statevalf,statplots,transform

(1)

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

R:=describegeometricmean1+10100,1+20100;evalf

R:=1253325

anova,describe,fit,importdata,random,statevalf,statplots,transform

(2)

which is (about)

evalf100R1

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;evalf

3325

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

describegeometricmean3,4

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:

1describegeometricmean13,14

12

(6)

but not with the arithmetic mean

describemean3,4

72

(7)

versus

1describemean13,14

247

(8)

See Also

describe(deprecated)[harmonicmean], describe(deprecated)[mean], describe(deprecated)[quadraticmean], Statistics, Statistics[GeometricMean], stats(deprecated)[data], transform(deprecated)[classmark]


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