VARIANCE in IDL

[ashmall(at)my-dejanews.com (Justin Ashmall)]

Dear All,

I have a question regarding the variance as calculated by IDL - I expect to 
get thoroughly flamed by some statistician types but I'm keen to know if I'm 
wrong!

I always thought the definition of variance was the mean of the squares of the 
differences from the mean, i.e.:

VARIANCE = { SUM [ (x - mean_x)^2 ] } / N 

and this is what I *thought* I was getting from IDL - it wasn't until I was 
testing a prog to calculate the means and variances of rows and columns of an 
array that I spotted that IDL's variance has N-1 as the denominator:

VARIANCE = { SUM [ (x - mean_x)^2 ] } / N-1

Now I realise the latter ( let's call it Var(n-1) ) is the best estimate of 
the variance of the overall population, if my data is a sample from that 
population, but that's not what I want (or expect) from the variance function.

More worrying is the fact that this isn't mentioned in any way in the on-line 
help for the VARIANCE function (although the equation does appear in the help 
on the MOMENT function). Perhaps a keyword to the function would be in order 
so you could select if you wanted "population estimate" or "sample" variance 
at the very least.

A simple example is given calculating Var(n) and Var(n-1) on the numbers 
1,2,3,4,5. The mean is obviously 3 but I would say the variance is 2.0 
(Var(n)), not 2.5 as given by IDL (Var(n-1)).

I'd be interested to hear if my definition of variance is correct and whether 
other people made the same assumption regarding variance as myself. 
Incidentally, I use IDL 5.1.1.

Thanks,

Justin