Please Note: This article is written for users of the following Microsoft Excel versions: 2007 and 2010. 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: Calculating a Geometric Standard Deviation.
by Allen Wyatt
(last updated September 12, 2016)
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:
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:
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:
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:
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 (11208) applies to Microsoft Excel 2007 and 2010. You can find a version of this tip for the older menu interface of Excel here: Calculating a Geometric Standard Deviation.
Excel Smarts for Beginners! Featuring the friendly and trusted For Dummies style, this popular guide shows beginners how to get up and running with Excel while also helping more experienced users get comfortable with the newest features. Check out Excel 2013 For Dummies today!
Need to sum a series of cells that fits some regular pattern? Here are several ways that you can get the summation that ...Discover More
Excel is very good at counting things, even when those things need to meet specific criteria. This tip shows how you can ...Discover More
Remember your number line from your early years in school? Some numbers can be below zero (negative numbers) and others ...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 ribbon interface (Excel 2007 or later)? This site is for you! If you use an earlier version of Excel, visit our ExcelTips site focusing on the menu interface.