On Sat, Jun 11, 2016 at 07:43:18PM -0400, Random832 wrote: > On Fri, Jun 10, 2016, at 21:45, Steven D'Aprano wrote: > > If you express your performances as speeds (as "calculations per > > second") then the harmonic mean is the right way to average them. > > That's true in so far as you get the same result as if you were to take > the arithmetic mean of the times and then converted from that to > calculations per second. Is there any other particular basis for > considering it "right"?
I think this is getting off-topic, so extended discussion should probably go off-list. But the brief answer is that it gives a physically meaningful result if you replace each of the data points with the mean. Which specific mean you use depends on how you are using the data points. http://mathforum.org/library/drmath/view/69480.html Consider the question: Dave can paint a room in 5 hours, and Sue can paint the same room in 3 hours. How long will it take them, working together, to paint the room? The right answer can be found the long way: Dave paints 1/5 of a room per hour, and Sue paints 1/3 of a room per hour, so together they paint (1/5+1/3) = 8/15 of a room per hour. So to paint one full room, it takes 15/8 = 1.875 hours. (Sanity check: after 1.875 hours, Sue has painted 1.875/3 of the room, or 62.5%. In that same time, Dave has painted 1.875/5 of the room, or 37.5%. Add the percentages together, and you have 100% of the room.) Using the harmonic mean, the problem is simple: data = 5, 3 # time taken per person mean = 3.75 # time taken per person on average Since they are painting the room in parallel, each person need only paint half the room on average, giving total time of: 3.75/2 = 1.875 hours If we were to use the arithmetic mean (5+3)/2 = 4 hours, we'd get the wrong answer. -- Steve _______________________________________________ Python-Dev mailing list Python-Dev@python.org https://mail.python.org/mailman/listinfo/python-dev Unsubscribe: https://mail.python.org/mailman/options/python-dev/archive%40mail-archive.com