In this article I showed some problems with the average or arithmetic mean and in this one I discussed alternatives including the trimmed mean, Winsorized mean, and median. But that does not exhaust the variety of measures of central tendency; there is the geometric mean, for one. Today, yet another measure of central tendency: The harmonic mean.

**What is the harmonic mean?**

The harmonic mean of the numbers through is defined as

For example, the harmonic mean of 1, 2 and 10 is (whereas the arithmetic mean would be

**When should I use the harmonic mean?**

One reason to use the harmonic mean is when you are averaging rates. Suppose, for example, that you drive 50 miles to work and home each day. Suppose that, one day, you travel to work at a speed of 50 miles per hour and travel home at 25 miles per hour. What is your average speed? The arithmetic mean is but that is not correct. The total distance traveled is 100 miles and the the total time is 3 hours, so the average should be 33.33; the harmonic mean gives this because it is

Great article! Glad to share it. Makes me wonder – would you be interested in a short article on KDE for measuring central tendency in the case of variable uncertainty? Averages are usually calculated by adding numbers up. However, if the numbers are measurements of some kind, the amount of uncertainty in the measurement can be different for each one. KDE treats each measurement as a distribution, not a discrete number, and adds the distributions. Let me know if you would like something (or just write it yourself – you know what I mean and your series of articles on central tendency is great!)