Where is the Harmonic mean used?

Question

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?

@mathlove Thank you for the link. – sevenOfNine Mar 04 '15 at 23:36 — sevenOfNine, Mar 04 '15 at 23:36

score 8 · Accepted Answer · answered Mar 04 '15 at 22:34

8

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.

answered Mar 04 '15 at 22:34

paw88789

40,402

Thank you very much. Your reply is very simple to understand for me. – sevenOfNine Mar 04 '15 at 23:36

score 1 · Answer 2 · edited May 23 '17 at 12:39

1

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

See this question as a reference:

https://stackoverflow.com/questions/34794664/how-should-i-calculate-the-average-speed-by-road-segment-for-multiple-segments/34795821#34795821

edited May 23 '17 at 12:39

Community

1

answered Oct 21 '16 at 20:59

Uri Goren

2,940

Where is the Harmonic mean used?

2 Answers2

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