[issue38382] statistics.harmonic_mean fails to raise error with negative input that follows a 0

[gaoxinge]

gaoxinge <gaoxx5 at gmail.com> added the comment:

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`.

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nosy: +gaoxinge

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Python tracker <report at bugs.python.org>
<https://bugs.python.org/issue38382>
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