The distribution of group sizes is not normal. It looks like a Normal Distribution that has been pushed to the left, with a long tail to the right. So the 68% rule for plus or minus one standard deviation isn't quite right, but it's also not far off. Also, there is no Central Limit Theorem for any measure of dispersion (range, SD, group size), so collections of data do not tend toward normality.
denton,
Could you elaborate on your reasoning here?
It's just a mathmatical truth.
If you are taking inteval/ratio data such as FPS, peak pressure, millimeters, etc., then Central Limit kicks in and the Distribution of Means will have a strong tendency toward normality. That is very convenient for users of the T Test and ANOVA because you don't usually have to worry much about the normality of the data, and the Standard Error of the Mean converges pretty quickly.
Switch to any measure of dispersion, and it's a different world. There is no tendency toward normality. The Distribution of Means looks just as awful as the raw data, and separating normal random variation from real change takes a lot bigger sample. If you're terminally curious, I could scan a page or two out of a text and post it for you.
So for interval/ratio data, we use T and ANOVA. For SD we use F, Bartlett, or Levene's Test.