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I am implementing some descriptive statistics in a program and would like to understand why the Harmonic Mean exists. What, precisely, does it achieve?

I have read this thread, but the answer has not resolved my query.

RobPratt
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GettingItDone
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  • I was going to say I wouldn't bother implementing the harmonic mean in statistics if I were you but apparently it's used in finance: https://en.wikipedia.org/wiki/Harmonic_mean#In_finance – Qiaochu Yuan Nov 21 '20 at 22:48
  • Most examples I have seen are set in a finance scenario. I can read the syntax, but don't understand why it matters or should be used. – GettingItDone Nov 21 '20 at 23:28

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Actually, in my opinion, the misapplication of statistics is a major issue.

From already presented examples, including the cited importance in the field of finance on calculating price earning ratios, for example, where the harmonic mean apparently can potentially play a key role (as in screening and more generally financial decision making) context is important.

Otherwise, one is just possibly contributing to potentially more misleading and even contextually deceptive statistical-based data.

My suggestion, have an embedded in your descriptive information summary (per links, an appendix, an expanded table, ...) an explanation of the particular statistic of interest along with key areas of its application. Consider also providing examples where it is expected to be likely not advisable.

And yes, the harmonic mean is more rarely referenced and exotic, but it can distinctly be decisively informative. Adding informational value will, in time, be well received.

AJKOER
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  • As the name might suggest the "harmonic mean" is important in music where it plays a part in constructing a "harmonic series" of notes. – user247327 Nov 21 '20 at 23:41