It actually doesn't require a normal distribution. If special causes like barrel rubs and shooter flinch have been eliminated, so that variation is random, then it will give about the same answer as calculating SD by its definition, the sum of squares. If special cause is present, then the classic sum of squares route will give a higher number.
Standard deviation is a measure of variation.
Range is a measure of variation.
They are different measures of the same thing, and can be converted back and forth. If the subgroups have few items, the conversion is pretty good.
If you are shooting five shots, range is about as good a number as you can get.
No, playing with some numbers here, I'm pretty sure it does require a normal distribution or at least an even spread of numbers across the range. Your assumptions don't hold up in the real world; velocity variation is not truly random and often shows skewed groupings that don't match your assumptions. Too many of the variables that affect velocity end up in groups (like different headstamps) and that makes an assumption of random data unrealistic.
For example, sometimes a first shot is lower velocity than all the rest in a string - the standard deviation is higher compared to another string of numbers with an even spread, even when the extreme spread is the same.
Or, maybe we have two lots of brass that result in different velocity, so we've got two velocity groups in our string - then the standard deviation is even higher with the same extreme spread.
We can't just assume those things don't happen (because they do), and that's why we don't just use e.s. by itself. Of course neither number means much with only 3 or 5 shots except to tell when something really went wrong.
