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.