To use this function, choose .

Calculates the geometric mean, which is a measure of central tendency that calculates an average of the data using multiplication instead of addition. For a set of n numbers, the geometric mean is the nth root of the product of those numbers. For example, the geometric mean of the numbers 2, 3, and 14 equals (2 * 3 * 14)^{1/3} = (84)^{1/3} = 4.

## Syntax

GMEAN(number)

For number, specify the column number. All values must be greater than 0.

## Example

Column |
Calculator expression |
Result |

C1 contains 6, 3, 15 |
GMEAN (C1) |
6.4633040701 |

## Uses

Use the geometric mean, not the arithmetic mean, when you need to determine the average of the factors in a product. For example, to determine the average rate of a return for an investment that earns 8% the first year and 52% the second year, calculate the geometric mean (1.08 * 1.52)^{1/2} ≈ 1.28 (an average return of 28%).

In statistics, the geometric mean (weighted) is used to determine the composite desirability in response optimization and the sample variance for Bartlett's test statistic for normal distributions.