There is a mean called Harmonic mean. http://dlmf.nist.gov/1.2#E19

I mostly see usage of arithematic mean and geometric mean. On the other hand, I have never seen the usage of Harmonic mean yet.

In what kind of case, is the Harmonic mean used?

  • $\begingroup$ See this. $\endgroup$
    – mathlove
    Mar 4, 2015 at 22:32
  • $\begingroup$ @mathlove Thank you for the link. $\endgroup$ Mar 4, 2015 at 23:36

2 Answers 2


You go on a round trip. You go out at $50$ miles per hour and come back at $60$ miles per hour. The average speed of your whole trip will be the harmonic mean of $50$ and $60$ (mph). You can extend this to several legs of a trip all the same length. Your overall average speed will be the harmonic mean of the speeds on the various legs of the trip.

  • $\begingroup$ Thank you very much. Your reply is very simple to understand for me. $\endgroup$ Mar 4, 2015 at 23:36

The harmonic mean usually appears when averaging speed (or rates in general).

See this question as a reference:



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.