To illustrate some of the comments others have made, suppose you are at the range with your trusty AR-15, and chronograph five shots: 3105, 3119, 3074, 3022, 3109.
The standard deviation is 30.43. But if we ran this same test over and over, under exactly the same conditions, 95% of the time we would get a standard deviation between 23.62 and 113.3 (Confidence Interval). In other words, as far as we can tell from five shots, the real long term standard deviation could easily fall anywhere in that range. The short version is, with only five shots, we have only a very imprecise estimate.
If we want to go to 99% CI, then we would say that the real answer could be anywhere between 20.46 and 173.3.
Variation is a slippery devil that does not want to be cornered and made to tell the truth. Sort of like some politicians we know.
If we apply the d2 rule, dividing the range, 97, by the d2 constant for n=5, we get an estimate of SD = 41.7, which is well within the Confidence Interval we got by the standard formula.
Last edited by denton; 08/02/20.
