RC20's observation can depend on the gun rather than the cartridge, based on the rate of muzzle rise that occurs while the bullet is still in the barrel.
The answer to the OP is that it depends on how certain you want to be that your answer is close to correct.
Correct what, exactly?
That takes a little explaining. The calculation your chronograph calls SD or just "s" is an estimate. What it estimates is the standard deviation of an infinite size sample (aka, a huge population) of the same thing. It's the standard deviation you are estimated to have if you could fire an infinite number of rounds of the same load in the same gun under the same conditions without that gun experiencing any wear. The error in the estimate narrows as the sample size increases because each additional sample is more likely to be representative than it is to be an outlier. So a larger sample accumulates a greater preponderance of representative members.
The statistical reason for making that estimate of what an infinite sample will do is to predict the future behavior of that ammo. Things like how many outliers you can expect and how often their different values will occur, or what an average group of x shots on a target will look like or to decide if one outlier in your velocities is likely to be so rare it should not be counted, etc.
This 3 min video explains it well. (and velocity does tend to have the normal distribution mentioned in the video). The practical reason for measuring velocity SD is that it is an indicator of consistency that can help with long-range accuracy, in particular, and help troubleshoot a number of problems that affect accuracy, especially irregular or inadequate primer seating, or powder that's going bad.
So, what sample size to use? SAAMI standards use 10 rounds for pressure standard deviations, but they are premised on a maximum allowed standard deviation (4% for HP rifle cartridges and 5% for handguns) plus two standard errors in the result. The two standard errors add 2.53% to the rifle average pressure and 3.16% to the handgun cartridge average pressures. The addition is to cover the fact the next set of ten is allowed to have an average value up to that greater total on the plus side.
The standard error is found by dividing the standard deviation by the square root of the number of rounds in the sample. It is a useful number because it is the estimated standard deviation of the mean result. It tells you 68% of the future 10-shot groups will have a mean (average) value within ±1 standard error and that 95% will be within ± two standard errors. So what you can do is take the standard deviation and divide it by the square root of your number of shots and see if that much error is acceptable to you? The bigger the number of shots in your group, the bigger that square root gets so, if you assume the standard deviation was estimated accurately by each calculation for the different sample sizes it will be the same for them all, so the error will get smaller as the group size increases.
The extreme spread will also vary with sample size. Ideally, it would not change the SD calculation, but in reality, as the group size gets too small, the odds of it accurately and uniformly representing the population get smaller. This leads to a problem with accuracy, too. The table below shows how extreme spread can be expected to vary with sample size out to the 95% limits. In other words, shooting multiple samples, expect 95% will stay somewhere between the red and blue lines where they cross the vertical line for your sample size.
Also, it is normal for your extreme spread to get bigger, on average, with larger samples because a larger sample offers more opportunities for the less probable outlying values to occur. That change will look like this:
So, when you increase your sample size from 3 to 10, the first chart shows the sample-to-sample ± scatter decreases, but the second chart shows the extreme spread will, on average, almost double. If, for example, the extreme spread in question was group size, your group sizes would be less different from one group to the next by a factor of 4, but the average size would be almost twice as big as your three-shot group sizes were averaging.
. It was good though to know how/why you use certain sample sizes to increase your 'confidence' in the results.... Not just for chrono results but when politicians, groups, start spouting stats, poll results, etc. .....