Can you give some examples where it's more representative? Average height? Average income? There are a lot of arguments in favor of median as a more intuitive replacement (and it is frequently used thus) but consider that:
a) Some people have ZERO income.
b) Either an odd or even number of people have NEGATIVE income.
Every day I deal in execution times, rounded to the nearest integral number of milliseconds. Lots of zeros.
A measure that is (a) not actually intuitively correct, (b) very hard to calculate in your head, and (c) useless for many, many non-trivial cases is NOT a good replacement for "linear mean" which is (a) often intuitively correct, (b) pretty easy to calculate in your head, and (c) always works, seems better.
Geometric mean also interacts with unit conversions which use a different zero-point. For instance, if you take the geometric mean of daily temperatures, you will get different means depending on whether you work in F or C or K.
a) Some people have ZERO income. b) Either an odd or even number of people have NEGATIVE income.
Every day I deal in execution times, rounded to the nearest integral number of milliseconds. Lots of zeros.
A measure that is (a) not actually intuitively correct, (b) very hard to calculate in your head, and (c) useless for many, many non-trivial cases is NOT a good replacement for "linear mean" which is (a) often intuitively correct, (b) pretty easy to calculate in your head, and (c) always works, seems better.