The leaders of our society, that is the inprint gunwriters, use three shot groups because the public accepts them as valid tests of accuracy. Which they are not. Gunwriters are paid a flat fee, according to DPris, $400 per article, and it is not in their financial interest to shoot too many expensive bullets! And, the less rounds are put down range, the less the chance of discovering the thunderstick in question don't shoot straight. That would affect advertising, and these periodicals make their profit through advertising. The subscription price is more or less, earnest money, and this has been the business model since the Ladies Home Journal of the 1880's.
If you really want to find out if the load is good, you have to get the round count up. I test cast bullet loads in my Marlin, and decided that "acceptable accuracy was to be found less than 1500 fps.
groups fell apart at 1600 fps
it turns out the first group was a statistical abnormally. This rifle does not shoot cast bullets worth a damn at any velocity. I had to get the round count up!
Group size and confidence is a hot topic among small bore prone shooters. I asked the number three guy in the Nation, at a Smallbore National Match, how many rounds does it take for him to have confidence in his ammunition. And he said a brick. (500 rounds) His rifle had been lot tested 90 times, and these lot tests are typically forty round groups, but you know, forty rounds does not reveal everything. And I agree, even with lot tested ammunition, until you get the round count up, you really don't know if lot tested ammunition is the stuff. I purchased a case of Eley Edge based on lot testing, and while the lot test indicated it was great stuff, it is not really great. My X counts are not as high as with other ammunition. It is good, but not great, and it took more than a brick to finally shake off the emotional high of the lot acceptance test, and realize what I was seeing on paper was real.