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.

Geometric Mean - dCode

Tag(s) : Mathematics, Data processing

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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.

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.

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

Example: 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.

Example: 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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