On I wrote:
See
http://en.wikipedia.org/wiki/Standard_deviation#Estimating_population_standard_deviation_from_sample_standard_deviation
as an example treatment which seems to conflict with the assertions
you have advanced in this last paragraph.
As I understand the wiki write up, even if you consider denominator
n=1 as valid for samples which do not represent the population,
you must still use denominator n=2 when you are dealing with
the population distribution.
I should have instead referenced the previous section
http://en.wikipedia.org/wiki/Standard_deviation#Standard_deviation_of_a_random_variable
--
Raul
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