Range (what shooters call ES) is directly convertible to standard deviation. As stated earlier, estimates at variation based on small samples can quite far off.
I'm not a statistician, but having been a theorem proving mathematician in a prior life I "feel a disturbance in the force" when I see something like that stated without the caveat hypotheses.
I could be wrong, but I think denton's statement is correct if we assume a normal distribution. Problem is, that's a poor assumption for this stuff. I've seen plenty of results in shooting that do not fit a normal distribution at all, with all sorts of common causes like mixed headstamp brass, mixed batches of components, etc. Theory like this falls apart when the assumptions don't match reality.
I don't worry about ES too much other than as an indication of inconsistent powder burn at low pressures. Otherwise I go by results on target and fine tune as needed.
