NumPy may give a nonzero variance (and thus standard deviation) for a constant array. This may be due to loss of numerical precision, but Pythons builtin variance routine gives the correct 0 answer, so clearly it's a preventable loss:

In [45]: x = [6715266981.538051]*10

In [46]: statistics.variance(x)
Out[46]: 0.0

In [47]: numpy.array(x).var()
Out[47]: 9.0949470177292824e-13

I think it would be highly desirable if x.std() and x.var() for a constant array could be assumed to be exactly identical to zero. I'm aware one should not compare floating point numbers but zero is a bit of a special case.