Tool to compute a geometric mean: an estimate of the tendency of the data in a list, it has the advantage of being less sensitive to high values.

Geometric Mean - dCode

Tag(s) : Statistics, Data Processing

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For a list of $ n $ values $ X = \{x_1, x_2, \dots, x_n\} $, the geometric mean is defined by the nth root ( $ \sqrt[n]{\dots} $ ) of the product of the values.

$$ \bar{x}_{geom} = \sqrt[n]{\prod_{i=1}^n{x_i}} $$

From a list of $ n $ values whose product (the multiplication of all the values) is $ p $, calculate the nth root of $ p $ that is $ \sqrt[n]{p} $.

__Example:__ The list of $ 3 $ numbers $ \{ 1, 10, 100 \} $ has for geometric mean $ \sqrt[3]{1 \times 10 \times 100} = 10 $, whereas it has for arithmetic mean $ 55.5 $.

To get a *geometric* representation, the geometric mean of the sides of a rectangle has a value $ c $ which could be the length of one side of a square of area identical to the original rectangle.

__Example:__ A rectangle of $ 6 \times 10 $ has an area of $ 60 $. The geometric mean of $ 6 $ and $ 10 $ is $ \approx 7.746 $. And a square of side length $ 7.746 $ has an area of $ \approx 60 $.

When the values are assigned coefficients, it is called a weighted geometric mean.

Using the mathematical formula: `//Python`

or to avoid a potential number overflow:

import numpy as np

def geometric_mean(iterable):

a = np.array(iterable)

return a.prod()**(1.0/len(a))`//Python`

import numpy as np

def geometric_mean(iterable):

a = np.log(iterable)

return np.exp(a.sum()/len(a))

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mean,number,geometric,list

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