🚀 go-pugleaf

I'd just like to add a couple of points to the many that have
been made. (More in the direction of people who are mathematically
sophisticated, but with little exposure to statistics. Unfortunately
this class remains sizeable.)

Firstly the ' n - 1 ' is really the dimension of a vector space:
the vector space of contrasts in the observations. In more complex
situations other numbers will appear in place of n -1. For example
if the observations come from several groups we are often 
interested in the within-group contrasts. Here we head towards the
idea of 'degrees of freedom'.

Secondly the ' n ' divisor is the one which makes the standard
deviation a functional on the space of empirical distribution
functions: if you take each observation twice the e.d.f. does not
change, and neither does the n-definition standard deviation.

For a lot of work in the theory of robust statistics and diagnostics
it is convenient to have statistics as functionals.

Both definitions are here to stay, as each leads to convenient
theory in different contexts.

-- 
Murray A. Jorgensen [ maj@waikato.ac.nz ]    University of Waikato
Department of Mathematics and Statistics     Hamilton, New Zealand      
__________________________________________________________________
'Tis the song of the Jubjub! the proof is complete,
if only I've stated it thrice.'