> do you have any comment on my previous answer?

I see what you're trying to do but think that interpretation is surprising
and is at odds with the existing and intended uses of the *xbar* argument.  

The goals were to allow the mean to be precomputed (common case) or to be recentered (uncommon).  Neither case should have the effect of changing the divisor.  

We can't break existing code that assumes that stdev(data) is equal to stdev(data, xbar=mean(data)).

>>> data = [1, 2]
>>> stdev(data)
0.7071067811865476
>>> stdev(data, xbar=mean(data))
0.7071067811865476