DOC: make difference between numpy behaviour clearer in Dataframe.std() and Series.std()

[timhunderwood]

Location of the documentation

https://pandas.pydata.org/pandas-docs/dev/reference/api/pandas.DataFrame.std.html
https://pandas.pydata.org/pandas-docs/dev/reference/api/pandas.Series.std.html

Documentation problem

The ddof kwarg has a different default to numpy. This means using the std() method on a Series or numpy.array with the same values give different results:

>>>df=pandas.Series([1,2,3])
>>>df.std()
Out[4]: 1.0
>>>df.values.std()
Out[5]: 0.816496580927726

Suggested fix for documentation

I assume the difference in behaviour is intentional, but I would suggest making this difference clearer in the documentation.

We could add the text: "Note that this normalization is different to numpy, which by default normalizes by N (equivalent to ddof=0)."
A similar string could be added in the kwarg description for ddof.

This would make it clear from reading the pandas docs that the behaviour is different to numpy, rather than having to compare the numpy docs side by side after noticing a discrepancy. It would also make users more likely to consider which ddof value they want for their use case.

If you agree, I am happy to make the PR to change this.

[MarcoGorelli]

Sure, go ahead (perhaps this would go well in a Notes section)