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
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