Function Repository Resource:

# GeothmeticMeandian

Calculate the geothmetic meandian of a list of numbers

Contributed by: Sander Huisman
 ResourceFunction["GeothmeticMeandian"][x1,x2,…] gives the geothmetic meandian of the xi. ResourceFunction["GeothmeticMeandian"][list] gives the geothmetic meandian of the elements in list.

## Details

As defined by the xkcd comic website, the geothmetic meandian is the number obtained by iteratively calculating {Mean[list],GeometricMean[list],Median[list]} to convergence.
For negative numbers, the geometric mean generally gives complex numbers. For complex numbers, the Median is modified so as to order by the absolute value of the numbers.

## Examples

### Basic Examples (1)

Compute the geothmetic meandian of some numbers:

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### Scope (3)

The input can be given as multiple arguments:

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The input can also be given as a list:

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The input can also contain complex numbers:

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### Possible Issues (2)

Due to the GeometricMean operation, negative numbers can result in complex answers:

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Sometimes a real result is returned:

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Symbolic values are not allowed and will be left unevaluated:

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### Neat Examples (1)

Find the distribution of the geothmetic meandian of 100 random variates of a normal distribution:

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SHuisman

## Version History

• 1.0.0 – 17 March 2021