In my article, “Measures of Central Tendency: How to go Wrong With the Mean,” I showed some problems with the average or arithmetic mean and in “Measures of Central Tendecy: The Trimmed Mean and Median,” I discussed alternatives including the trimmed mean, Winsorized mean, and median. But that does not exhaust the variety of measures of central tendency. One other measure is the geometric mean.
What is the geometric mean?
The geometric mean of numbers is defined as which may not be particularly clear. In words, rather than adding the numbers and then dividing by the number of numbers (the arithmetic mean) we multiply the numbers and then take the nth root of the product.
Example of calculating the geometric mean
Suppose we have numbers: 1, 2, 3, 4, 5. The geometric mean of these numbers is . In this example, it is very close to the arithmetic mean of 3.
When to use the geometric mean?
One reason to use the geometric mean is if you are averaging things that are on different scales. Suppose, for example, you are a college admissions officer. You have students’ SAT scores and their grade point averages. But the SAT score ranges from 0 to 1600 (if you combine the two) and the GPA from 0 to 4. If you want them to be equally weighted, use the geometric mean. Suppose that Joe got 1550 on his SAT and has a 3.0 GPA. Bill, on the other hand, has a 1500 on his SAT and a 4.0 GPA. If we take the arithmetic mean then Joe gets while Bill gets an . Yet it seems like Bill’s scores ought to be better than Joe’s…. With the geometric mean Joe gets while Bill gets
In my next post, I will look at yet another measure of central tendency: The Harmonic Mean.