David MacIver added the comment:

I'm not sure what you mean by float having a limit here. It's certainly finite 
precision, but there is still a representable value with that finite precision 
closest to the mean.

As an example where there is an obvious correct answer that will trigger this 
error: statistics.mean([sys.float_info.max, sys.float_info.max]), this should 
return sys.float_info.max (which is definitely representable!), but instead 
raises this overflow error.

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Python tracker <rep...@bugs.python.org>
<http://bugs.python.org/issue25177>
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