I voted yes, but now I’m not so sure because I thought it was the geometric mean. I have absolutely no idea whether I (as a person with an MA in mathematics) was ever formally taught about this particular mean.
Ditto. I should have voted no: I knew of the geometric, but not harmonic.
I always associated “arithmetic” with linear operations, while “geometric” suggests areas and volumes; quantities obtained through multiplication.
A silly anecdote: I sometimes try to amuse myself while driving trying to compute various averages for speed and fuel consumption (and although I use harmonic means often in my work it never occurred to me that an average of speed taken over the time variable was the same as the harmonic average of the speed taken over distance, so thanks, robardin). I was trying to explain this to someone and was getting nowhere until I realized that he was taking my (idiosyncratic?) use of “average over” to indicate straight division rather than shorthand for a normalizing variable. Yes, I’m a real hit at parties.
Pretty sure it came up in single variable calculus at some point.
It never came up at school or university for me either. I only know about the concept because that’s how Baseball-Reference.com calculates its “Power-Speed number” statistic (the harmonic mean of the number of home runs and stolen bases).
You know, in writing that up I realized that that point is made very clearly (if not obviously) in the Wikipedia summary: Equivalently, the harmonic mean is the reciprocal of the arithmetic mean of the reciprocals.
In other words, any time you would need to “flip” (reciprocate) a ratio to get the denominators into the same context before taking a straight average (arithmetic mean), followed by having to re-reciprocate the resulting average to get back to the desired unit of rate (as in my example, converting distance-per-time for different times over the same distance into a time-per-distance unit)… you can use the harmonic average to do it in one step.
Well, one step only in that you’re calling the whole chain of things by a single name. It’s not like calling it “the harmonic mean” actually makes calculating it any simpler, though.
I’m a sciency guy, but no, I’ve never heard of it.
Thanks for the wiki link, I’ve got all sorts of data I’d like to try applying it to 