I think that three kinds of mean should behave like:

- `geometric mean`: input should be float, finite and positive
- `harmonic mean`: input should be float, finite and nonzero
- `mean` or `fmean`: input should be float, finite

Otherwise these mean functions should raise a `StatisticsError`. 

Two points that we should pay attention to:

- Why every input should be float? Because it is a statstics library, we should focus on the float instead of complex number or string or `math.nan`.

- Why every input shoud be finite? Becuse we should get rid of `math.inf`.