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The average of several 5shot groups only tells you the average of several 5shot groups, and that's a completely arbitrary statistic.

I suppose that choosing to fire 5 shot groups and average 5 of them is just as arbitrary as choosing to fire 25 shots into a single group. The result of either one is only representative of the results of that particular procedure.
Similarly, someone firing 40 shots in a single group, or choosing to average three 10 shot groups should expect to find that the results of their arbitrary choices will not be representative of firing a 25 shot group or choosing to average five 5 shot groups.
Of course, all of that is really neither here nor there.
The point is that if you shoot a large number of shots into one group and make one mistake, it is the mistake that is going to dominate the results. If you fire more groups and average the results, a single mistake can only affect one group and the effect of averaging will reduce the impact of that mistake in the overall results.
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If the point is to determine how you, your gun or ammo perform, the most important statistic is the largest group, not the average or the smallest.

If the point is to determine how you, your gun or the ammo perform
on average, then the important statistic is the average performance.
If the point is to determine how you, your gun or the ammo perform
in the worst case, then, of course, the most important statistic is the largest group.
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There is a problem with taking multiple small samples. They can, by chance, not represent the actual performance you're really trying to test.

The nice thing about the averaging process is that if you take enough samples, the odds become good that the average results are representative of the typical performance for that particular course of fire.
On the other hand, if you put all your eggs in one basket and that result turns out to be atypical, you have spent a lot of work on a result that doesn't tell you much.