Please Note: This article is written for users of the following Microsoft Excel versions: 2007, 2010, and 2013. If you are using an earlier version (Excel 2003 or earlier), this tip may not work for you. For a version of this tip written specifically for earlier versions of Excel, click here: Using GEOMEAN with a Large List.

Using GEOMEAN with a Large List

by Allen Wyatt
(last updated July 31, 2018)

4

Ken wrote about a problem he was having with the GEOMEAN function. When he attempts to use the function on a large number of values (3,500 rows of data), he gets a #NUM error value returned.

The GEOMEAN function is used to return the geometric mean of a series of values. The GEOMEAN of n numbers is the n-th root of the product of the numbers. For example, if there are four values in a series (A through D), then the product of those numbers is A * B * C * D, and the GEOMEAN is the fourth root of that product.

The #NUM error would be return if any of three conditions were met: any of the values was equal to zero, any of the values was negative, or the limits of Excel were exceeded. It is likely that it is this last condition that Ken is running into, particularly if any of his 3,500 values are large.

Since GEOMEAN finds the product of the 3,500 numbers (multiplies them all by each other) and then takes the nth root, the product may easily be too large for Excel. The largest positive number in Excel is 9.99999999999999 * 10^307 (in scientific notation this is written as 9.99999999999999E+307). If the product gets larger than this number you will get a #NUM error for the function.

The solution is to use logs to do the calculation. This is easiest to understand when you look at a transformation of the GEOMEAN function:

GEOMEAN = (X1*X2*X3*...*Xn)^ (1/n)
ln(GEOMEAN) = ln((X1*X2*X3*...*Xn)^ (1/n))
ln(GEOMEAN) = (1/n) * ln(X1*X2*X3*...*Xn)
ln(GEOMEAN) = (1/n) * (ln(X1)+ln(X2)+ln(X3)+...+ln(Xn))
ln(GEOMEAN) = average(ln(X1)+ln(X2)+ln(X3)+...+ln(Xn))
GEOMEAN = exp(average(ln(X1)+ln(X2)+ln(X3)+...+ln(Xn)))

If you follow through the above, you see that GEOMEAN is equivalent to the exponent of the average of the logs of the values. You can calculate the desired result by using the following array formula instead of the GEOMEAN function:

=EXP(AVERAGE(LN(A1:A3500)))

This assumes that the desired values are in the range A1:A3500. Since it is an array formula, you must enter it into a cell by using Ctrl+Shift+Enter.

ExcelTips is your source for cost-effective Microsoft Excel training. This tip (9328) applies to Microsoft Excel 2007, 2010, and 2013. You can find a version of this tip for the older menu interface of Excel here: Using GEOMEAN with a Large List.

Author Bio

Allen Wyatt

With more than 50 non-fiction books and numerous magazine articles to his credit, Allen Wyatt is an internationally recognized author. He is president of Sharon Parq Associates, a computer and publishing services company. ...

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Comments

If you would like to add an image to your comment (not an avatar, but an image to help in making the point of your comment), include the characters [{fig}] in your comment text. You’ll be prompted to upload your image when you submit the comment. Maximum image size is 6Mpixels. Images larger than 600px wide or 1000px tall will be reduced. Up to three images may be included in a comment. All images are subject to review. Commenting privileges may be curtailed if inappropriate images are posted.

What is nine less than 9?

2016-06-13 15:31:35

Candan

I see now that I missed the sentence about it being an array formula. Feel free to disregard my earlier comment.


2016-01-06 17:55:52

Miguel R

Thanks! I used it for 3,700 rows of data!


2015-04-14 13:45:52

Randall

How or could you use the AVERAGEIFS function on multiple conditions instead of the AVERAGE ?

=EXP(AVERAGE(LN(A1:A3500)))


2014-05-23 17:15:38

Jim Adams

Thank you so much for your instructions on this, they were very helpful.

Jim


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