Mule Deer is right. On average, 5 shot groups will be 1.27 X the size of 3 shot groups. It comes from the fact that as you add shots, the group size never gets smaller and sometimes gets larger.
The old saw about needing 30 items for statistical significance is something that comes up a lot. Actually, that's the minimum number of samples needed for Z tests to work. Everybody gets taught that in college stats, and for some reason it sticks. It's not too important, because practically nobody uses Z tests since the invention of the T Test back in about 1925. College courses are slow to change. If colleges offered careers in hunting, I swear we would be learning about the 50 Sharps and the best place to shoot a bison.
People who favor 3-shot groups are usually asking the wrong question. They often seem to reason that they never shoot more than 3 shots at a critter. The better question is, how well does a 3 shot group predict future performance of the firearm? The answer is, not very well at all.
The average of three 5-shot groups is a decent estimate of the long term accuracy of the rifle. I'd have to look back at my notes, but IIRC that will get you a plus or minus 25% estimate. Getting a much better number than that requires a lot more shooting.
