HARMEANZ Function

Returns the harmonic mean, using zero fuzzing.

Category:

Descriptive Statistics

Syntax

HARMEANZ(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 all the arguments are missing values, then the result is a missing value. Otherwise, the result is the harmonic mean of the nonmissing values.

If any argument is zero, then the harmonic mean is zero. Otherwise, the harmonic mean is the reciprocal of the arithmetic mean of the reciprocals of the 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 harmonic mean is

\begin{matrix} \frac{n}{\frac{1}{x_{1}} + \frac{1}{x_{2}} + \dots + \frac{1}{x_{n}}} \end{matrix}

Comparisons

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

Example

The following SAS statements produce these results.

SAS Statement	Result
x1=harmeanz(1,2,4,4);	2
x2=harmeanz(.,4,12,24);	8
x3=harmeanz(of x1-x2);	3.2