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Geometric Mean

Tool to compute a geometric mean. The geometric mean of a list of numbers is a representation which gives 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) : Mathematics, Data processing

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# Geometric Mean

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## Weighted Geometric Mean Calculator

Tool to compute a geometric mean. The geometric mean of a list of numbers is a representation which gives an estimate of the tendency of the data in a list, it has the advantage of being less sensitive to high values.

## Answers to Questions

### How to compute an arithmetic mean?

Consider 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.

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

The list of $$4$$ 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, if we take the geometric mean of the sides of a rectangle, then we find a value $$c$$ which could be the length of one side of a square of area identical to the original rectangle.

Consider a rectangle of $$6 \times 10$$, with 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.

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