There are situations in which just one of the arithmetic, geometric, and harmonic means are appropriate to use an the other two are meaningless.
Is there any situation which more than one of these means are meaningful and have good interpretations?
Thanks.
There a lot of means (http://en.wikipedia.org/wiki/Mean). In engineering, some fundamental equations involve equations in which the logarithmic mean is used and this is a quite expensive operation; so, some people found very nice approximations based on a linear combination of arithmetic and geometric means. If you are interested, let me know; we should continue.