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Geometric Mean

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.

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Geometric Mean -

Tag(s) : Statistics, Data Processing

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# Geometric Mean

## Weighted Geometric Mean Calculator

### What is a geometric mean? (Definition)

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.

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

### How to compute a geometric mean?

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.

### How to program/code a geometric mean function?

Using the mathematical formula: //Pythonimport numpy as npdef geometric_mean(iterable): a = np.array(iterable) return a.prod()**(1.0/len(a)) or to avoid a potential number overflow://Pythonimport numpy as npdef geometric_mean(iterable): a = np.log(iterable) return np.exp(a.sum()/len(a))

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