Well I got this one wrong, mainly because the SQL function naming is a little bizarre:

STDEV is the estimated Population Standard Deviation (although there's no P in the name)

STDEVP is the actual Sample Standard Deviation (although there is a P in the name)

I thought the P in STDEVP stood for "Population", so STDEVP would be the estimated Population Standard Deviation (obtained by applying Bessel's correction to the actual Sample Standard Deviation) and STDEV the actual Sample Standard Deviation (in the SQL 2000 days you could look it up in BoL, so I never bothered to learn it - I wanted those functions rarely enough for it not to be worth making an effort to learn it); when I discovered that which is which isn't documented (at least not in any obvious manner) in BoL for SQL 2008 I just tried to work out which was which based on the name, and got it wrong because the SQL function names are misleading.

You can't apply Bessel's correction when your sample has only 1 member, so SQL Server quite correctly refuses to attempt it. Actually it would be better to return an appropriate error (one that specifically means that STDEV has been applied to a singleton sample) than to return NULL. Returning NULL is better than returning a zero-divide error which might be caused by some other part of a select statement - eg if SELECT STDEV((a+c)/b) FROM T where a > 37 returned a zero-divide error one couldn't tell whether the error occurred because one of the b attributes was zero or because there was at most one row with a > 37. But returning NULL means you don't know whether the sample was empty or a singleton, which is why a specific error should be returned (ideally a specific error should be returned instead of NULL for the empty sample case too, but that is another story, part of a much more general one).