Statistics Calculator: Geometric Mean

Calculate the geometric mean from a set of positive or negative numerical values.

Data is from: Population Sample

Geometric Mean Calculator

How to use this calculator

This calculator will find the geometric mean of a set of numbers.

Enter the numerical values in the box above. The numbers (either all positive or all negative) must be separated by commas or spaces, or they may be entered on separate lines. The population or sample option selector is only used for calculating the variance or standard deviation. For the calculation of the geometric mean it is irrelevant and may be ignored. Press the "Submit Data" button to retrieve the result. The geometric mean will be displayed above together with links to calculate other measures using the same set of data. Press "Reset" to clear the data and start again.

What is the geometric mean

The geometric mean, sometimes referred to as geometric average of a set of numerical values, like the arithmetic mean is a type of average, a measure of central tendency.

Due to the formula used to calculate it, all values in the dataset must have the same sign, that is, they must be all positive or all negative. Also, if the dataset contains a 0, the geometric mean will always be 0.

Geometric mean formula

This calculator uses the following formula to calculate the geometric mean:

$ \bar{x}_g = \left( \prod_{i=1}^n x_i \right)^\frac{1}{n} $

where n is the total number of values and xi (x2, x1, ... ,xn) are the individual numbers in the data set. The formula is equivalent to:

$ \sqrt[n]{x_1 \cdot x_2 \cdot ... \cdot x_n} $

In other words: It's the nth root of the product of n values.