**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: Calculating a Geometric Standard Deviation.

Jim has a set of data on which he needs to calculate some statistical information. He uses built-in Excel functions to calculate many of these, such as the geometric mean. He cannot seem to figure out how to calculate the geometric standard deviation, however.

The place that a geometric mean is most often used (and, therefore, a geometric standard deviation) is when calculating investment returns over time, especially when the returns involve compound interest. How you calculate the geometric mean is rather easy—you use the GEOMEAN function built into Excel. How you calculate a geometric standard deviation, however, depends on which resource you are referencing.

One reference that explains the math behind a geometric standard deviation is found on Wikipedia:

http://en.wikipedia.org/wiki/Geometric_standard_deviation

Let's assume that you have calculated the compound annual growth rate for an investment for four years. Over those four years the rate is expressed as 1.15 (+15%), 0.9 (-10%), 1.22 (+22%), and 1.3 (+30%). If you place these values in cells A1:A4, then apply the simplest form of calculating geometric standard deviation found on the Wikipedia page, you would enter the following as an array formula:

=EXP(STDEV(LN(A1:A4)))

This provides a result of 1.1745, rounded to four decimal places. However, there is some muddiness, as evidenced in this mathematical treatise at the Motley Fool:

http://www.fool.com/workshop/2000/workshop000309.htm

Note that it references the results of the above formula as the "standard deviation of the log values," insisting that you need to add the average of the log values to the standard deviation and then use the EXP function, in this manner:

=EXP(STDEV(LN(A1:A4))+AVERAGE(LN(A1:A4)))

Again, this must be entered as an array formula. It provides a result of 1.3294, which is significantly different from what is returned using the simpler formula from Wikipedia. Which is the actual geometric standard deviation is apparently a matter of debate and, perhaps, dependent on a definition of terms.

*ExcelTips* is your source for cost-effective Microsoft Excel training.
This tip (11207) 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: **Calculating a Geometric Standard Deviation**.

**Solve Real Business Problems** Master business modeling and analysis techniques with Excel and transform data into bottom-line results. This hands-on, scenario-focused guide shows you how to use the latest Excel tools to integrate data from multiple tables. Check out *Microsoft Excel 2013 Data Analysis and Business Modeling* today!

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 a ...

Discover MoreWhen you need to count a number of cells based upon a single criteria, the standard function to use is COUNTIF. This tip ...

Discover MoreWhen performing a statistical analysis on a large dataset, you may want to use GEOMEAN to figure out the geometric mean of ...

Discover More**FREE SERVICE:** Get tips like this every week in *ExcelTips,* a free productivity newsletter. Enter your address and click "Subscribe."

2016-02-07 17:12:58

Javier

The formula in the wikipedia is the real geometric standard deviation

What happens is that the geo. std. dev. by definition is expressed in multiplicative terms, like everything relative to geometric stuff.

So Todd at fool.com just converted it to an non relative geo. std. dev. for the shake of comparison. He just multiplied the geo. std. dev. by the geo. mean to get it.

=EXP(STDEV(LN(A1:A4)))*EXP(AVERAGE(LN(A1:A4)))

is equal to:

=EXP(STDEV(LN(A1:A4))+AVERAGE(LN(A1:A4)))

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.

**FREE SERVICE:** Get tips like this every week in *ExcelTips,* a free productivity newsletter. Enter your address and click "Subscribe."

Copyright © 2017 Sharon Parq Associates, Inc.

## Comments