Geometric Mean Calculator

On this page the geometric mean of a series of numbers is calculated. The geometric mean is the mean, which is obtained by taking the n-th root from the product of n numbers.

To perform the calculation, enter a series of numbers. Then click the 'Calculate' button. The list can be entered unsorted.

Input format

The data can be entered as a series of numbers, separated by semicolons or spaces. You can enter the data as a list (one value per line). Or from a column from Excel spreadsheet by copy & paste

The geometric mean is the mean, which is obtained by taking the n-th root from the product of n numbers. The geometric mean is always less than or equal to the arithmetic mean.

Im Gegensatz zum arithmetischen Mittel ist das geometrische Mittel nur für nichtnegative Zahlen geeignet und nur für echt positive reelle Zahlen sinnvoll, denn wenn ein Faktor gleich null ist, ist schon das ganze Produkt gleich null. Für komplexe Zahlen wird es nicht eingesetzt, da die komplexen Wurzeln mehrdeutig sind.

In contrast to the arithmetic mean, the geometric mean is only suitable for non-negative numbers and only makes sense for truly positive real numbers, because if a factor is equal to zero, the entire product is already equal to zero. It is not used for complex numbers because the complex roots are ambiguous.

Geometric mean formulas

This average is calculated by taking the n^th root from the product of n numbers.

\(\displaystyle \overline{x}_{geom} =\sqrt[n]{x_1 · x_2 · ... · x_n} = \sqrt[n]{\prod^n_{i=1} x_i} \)

Example

In the following example we calculate the geometric mean of the 5 numbers

\(\displaystyle 5,3,4,2,6 \)

To do this, the numbers are multiplied and the 5th root is taken from the product.

\(\displaystyle \overline{x}_{geom} =\sqrt[5]{5 · 3 · 4 · 2 · 6}≈ 3.7279 \)

More statistics functions

Arithmetic Mean • Contraharmonic Mean • Covariance • Empirical distribution CDF • Deviation • Five-Number Summary • Geometric Mean • Harmonic Mean • Inverse Empirical distribution CDF • Kurtosis • Log Geometric Mean • Lower Quartile • Median • Pooled Standard Deviation • Pooled Variance • Skewness (Statistische Schiefe) • Upper Quartile • Variance