GEOMEANZ Function

Returns the geometric mean, using zero fuzzing.

Category:

Descriptive Statistics

Syntax

GEOMEANZ(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

n

be the number of arguments with nonmissing values, and let

x_{1}, x_{2}, \dots, x_{n}

be the values of those arguments. The geometric mean is the

n^{t h}

root of the product of the values:

\begin{matrix} \sqrt[n]{(x_{1} * x_{2} * \dots * x_{n})} \end{matrix}

Equivalently, the geometric mean is

\begin{matrix} \exp (\frac{(\log (x_{1}) + \log (x_{2}) + \dots + \log (x_{n}))}{n}) \end{matrix}

Comparisons

The MEAN function returns the arithmetic mean (average), and the HARMEAN function returns the harmonic mean, whereas the GEOMEANZ function returns the geometric mean of the nonmissing values. Unlike GEOMEAN, GEOMEANZ does not fuzz the values of the arguments that are approximately zero.

Example

The following SAS statements produce these results.

SAS Statement	Result
x1=geomeanz(1,2,2,4);	2
x2=geomeanz(.,2,4,8);	4
x3=geomeanz(of x1-x2);	2.8284271247