Please Note: This article is written for users of the following Microsoft Excel versions: 97, 2000, 2002, and 2003. If you are using a later version (Excel 2007 or later), this tip may not work for you. For a version of this tip written specifically for later versions of Excel, click here: Using GEOMEAN with a Large List.
by Allen Wyatt
(last updated April 11, 2015)
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:
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 (2580) applies to Microsoft Excel 97, 2000, 2002, and 2003. You can find a version of this tip for the ribbon interface of Excel (Excel 2007 and later) here: Using GEOMEAN with a Large List.
Professional Development Guidance! Four world-class developers offer start-to-finish guidance for building powerful, robust, and secure applications with Excel. The authors show how to consistently make the right design decisions and make the most of Excel's powerful features. Check out Professional Excel Development today!
Excel is used by many people to hold all sorts of data, not just numbers. If you have cells that include meaningful ...Discover More
Need to find the lowest numbers in a range of values? It's easy to do using the SMALL worksheet function, or you can use ...Discover More
When you need to count a number of cells based upon a single criteria, the standard function to use is COUNTIF. This tip ...Discover More
FREE SERVICE: Get tips like this every week in ExcelTips, a free productivity newsletter. Enter your address and click "Subscribe."
Got a version of Excel that uses the menu interface (Excel 97, Excel 2000, Excel 2002, or Excel 2003)? This site is for you! If you use a later version of Excel, visit our ExcelTips site focusing on the ribbon interface.