# HARMEAN function

Returns the harmonic mean of a data set. The harmonic mean is the reciprocal of the arithmetic mean of reciprocals.

Syntax

HARMEAN(number1,number2,...)

Number1, number2, ...     are 1 to 255 arguments for which you want to calculate the mean. You can also use a single array or a reference to an array instead of arguments separated by commas.

Remarks

• The harmonic mean is always less than the geometric mean, which is always less than the arithmetic mean.
• Arguments can either be numbers or names, arrays, or references that contain numbers.
• Logical values and text representations of numbers that you type directly into the list of arguments are counted.
• If an array or reference argument contains text, logical values, or empty cells, those values are ignored; however, cells with the value zero are included.
• Arguments that are error values or text that cannot be translated into numbers cause errors.
• If any data point ≤ 0, HARMEAN returns the #NUM! error value.
• The equation for the harmonic mean is:

Example

The example may be easier to understand if you copy it to a blank worksheet.

• Create a blank workbook or worksheet.
• Select the example in the Help topic.

Note   Do not select the row or column headers.

Selecting an example from Help
• Press CTRL+C.
• In the worksheet, select cell A1, and press CTRL+V.
• To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.
A
Data
4
5
8
7
11
4
3
Formula Description (Result)
=HARMEAN(A2:A8) Harmonic mean of the data set above (5.028376)

Applies to:
Excel 2007