Jordan Smith has exactly correctly described the difference between sample and population.
Also, standard deviation is a biased estimator, not an unbiased one. On average, it will underestimate dispersion, particularly with small samples. Variance and range are unbiased.
The uncertainty in any estimate of variation with as few as 5 samples is surprisingly large. SD is a lot harder to pin down than averages are.
Think of "the population" as the collection of all the velocities of all possible shots with the load being tested. When you go to the range and fire ten shots and record their velocities you have drawn a sample from the population. When you average the ten velocities you get a sample mean which is an estimate of the population mean. When you calculate the standard deviation for your sample you have a sample SD which is an estimate of the population SD.
Jordan Smith has exactly correctly described the difference between sample and population.
Also, standard deviation is a biased estimator, not an unbiased one. On average, it will underestimate dispersion, particularly with small samples. Variance and range are unbiased.
The uncertainty in any estimate of variation with as few as 5 samples is surprisingly large. SD is a lot harder to pin down than averages are.
It depends on what you determine to be your confidence interval value. Is a 95% confidence interval apply to velocity calculations? I took several classes in statistics and modeling in college, but I never gave much thought to how they apply to shooting statistics, for some reason.
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.
.......... Interesting thread here, but this dinosaur now just worries about ES, because if it's not big the SD is better too. I was never destined to be a mathematician.
Calculating SD on a 5 shot group is only better than having no data at all, but if it makes you happy & all warm & fuzzy, then please, carry on.
MM
A little off topic, that's one of the benefits of a labradar. We can shoot a sixty round plus sighters match and run the numbers of the large data set.
Where I come from, the standard for meaningful data calculation of SD & CpK values is n=30.
MM
In the data I worked with doing research, sample sizes smaller than 500 were considered suspect and insignificant for anything other than general trending.
That comes from the rudimentary Z test, which assumes that you know the true population mean. And, you do need about 30 samples to be sure you're close to meeting that assumption.
Nobody does Z tests, except in a classroom. Since the 1920s, everybody does the T Test instead. That assumes that all you have is an estimate of the true mean, based on a sample. And that removes the requirement to have at least 30 data.
Cpk depends on an estimate of the mean, plus an estimate of standard deviation. Incidentally, it uses the d2 method of estimating standard deviation. It can take a lot more than 30 samples to nail down the SD.
For some reason, n=30 sticks in everyone's mind. But it only applies in one narrow situation.
As a couple of people have noted, an estimate of SD based on a sample of five is very imprecise.
Read up on what denton wrote, understand, apply to your industry examples safe them millions in r&d funds and make a mint as a consultent, then. You are welcome.
After 25 years of consulting and training in the quality and process improvement field, I've seen it too, and worse.
It's just not the most productive choice. Sometimes you need more, and sometimes you need less. Once in a while, 30 does actually work out to be the right answer.
