# Geometric mean | Statistics

The geometric mean is a special form of central value that is useful when we have to calculate the average of the percentages, ratios, indices and growth rates.

The geometric mean is calculated as the n:th root of the product of n values.

Geometric mean, 10 observations:

10th root of (1.05 * 1.07 * 1.08 * 1.10 * 1.12 * 1.12 * 1.13 * 1.14 * 1.15 * 1.18)

The geometric mean will always be less than or equal to the normal mean. All the values has to be positive for the geometric mean to be calculated. The geometric mean is used frequently in business administration and economics.

The geometric mean can also be used to calculate the average return over time. Average yield is calculated as the n:th root of the value at the end of the period divided by the value at start of the period.

Average yield per year, 10 years: 10th root of (10 000/1 000)

Updated

4/30/2013

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geometric mean, statistics