Geometric Mean

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]{} $ ) of the product of the values.

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

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
import numpy as np
def geometric_mean(iterable):
a = np.array(iterable)
return a.prod()**(1.0/len(a))
or to avoid a potential number overflow://Python
import numpy as np
def geometric_mean(iterable):
a = np.log(iterable)
return np.exp(a.sum()/len(a))