# GEOMEAN Function

Returns the geometric mean.

 Category: Descriptive Statistics

## Syntax

GEOMEAN(argument<,argument,…> )

### Required Argument

#### argument

is a nonnegative numeric constant, variable, or expression.

 Tip The argument list can consist of a variable list, which is preceded by OF.

## Details

If any argument is negative, then the result is a missing value. A message appears in the log that the negative argument is invalid, and _ERROR_ is set to 1. If any argument is zero, then the geometric mean is zero. If all the arguments are missing values, then the result is a missing value. Otherwise, the result is the geometric mean of the nonmissing values.
Let $equation$ be the number of arguments with nonmissing values, and let $equation$ be the values of those arguments. The geometric mean is the $equation$ root of the product of the values:
$equation$
Equivalently, the geometric mean is
$equation$
Floating-point arithmetic often produces tiny numerical errors. Some computations that result in zero when exact arithmetic is used might result in a tiny nonzero value when floating-point arithmetic is used. Therefore, GEOMEAN fuzzes the values of arguments that are approximately zero. When the value of one argument is extremely small relative to the largest argument, then the former argument is treated as zero. If you do not want SAS to fuzz the extremely small values, then use the GEOMEANZ function.

## Comparisons

The MEAN function returns the arithmetic mean (average), and the HARMEAN function returns the harmonic mean, whereas the GEOMEAN function returns the geometric mean of the nonmissing values. Unlike GEOMEANZ, GEOMEAN fuzzes the values of the arguments that are approximately zero.

## Example

The following SAS statements produce these results.
SAS Statement
Result
`x1=geomean(1,2,2,4);`
`2`
`x2=geomean(.,2,4,8);`
`4`
`x3=geomean(of x1-x2);`
`2.8284271247`