Reiterating here - the inherent variability of a population, a data set, dictates the sample volume required to establish whether the sample set is truly representative (statistically valid) of the population, or not (statistically invalid).
@denton mentioned the decreasing value in additional shots fired between 5 and 10 in another thread this week - entitled “5 shot groups are near worthless” or something of the sort.
We do have the complication that not all error sources in rifle shooting follow Gaussian/Normal distributions - not all errors present a “bell curve” - ESPECIALLY not mechanical errors by the shooter (these can be “on/off,” bi-nodal, with a relatively bell shaped node happening at each position, for example, flinching vs. not for some shots, or slapping trigger vs. follow through, OR they may be directionally biased, for example, ignoring wind, or jerking a trigger which is always in one direction, or subconsciously favoring an imbalance sight picture, or parallax via improper head position).
So Gaussian statistics don’t always offer applicable predictability, but we do know, if a shooter is putting up big groups, they need more shots to define their variance and confidence intervals. We really have to identify which are the dominating sources of error, and analyze the system to determine the appropriate number of shots - in general, we know it’s more than 1 shot per group, but stating a validity threshold of 3 or 5 or 10 or 50 really isn’t sensible - because what is valid for one population (data set) may not be valid for another. I’ve had systems which required more than 50 samples to approach differentiated data between step changes. We really can’t assign blindly that “5 isn’t enough, you need 10,” just the same as we shouldn’t blindly assume “10 is always better than 5.”