It sounds snarky, but it's true - all three shot groups are triangles. You can't shoot a round three shot group - it's a triangle. (side note- if your horizontal group is not due to wind, you've got an out of tune rifle).
To add to Donovan's post above, which is totally accurate, the context for it is gaining confidence that a load is as good as you think it is. If you have a load that you think is good, and you want to confirm it and you only have 15 rounds, you're better off shooting 3 five-round groups than 5 three-round groups or 1 fifteen-shot group. That last one may sound counter-intuitive, but it's true. It has to do with the information contained in each group - which is the two most extreme shots that define the groups size (obviously), but also the fact that every other shot landed in between them. So when you shoot 15 shots, you get 2 extreme shots, and 13 in between. When you shoot 3 five-round groups, you get 6 extreme shots, and 9 in between. The math works out that the best balance is around 5 shots/group.
The reason we can get away with three-shot groups when developing loads is that we typically do it in a systematic way - one group per charge, stepped up by .4 grains at a time, for example. There is information in that beyond the size of the groups - there is a known relationship between charge weight vs group size (for example) that adds confidence, so the three-shot groups are better than they would be if they were truly independent. So using three shot groups (instead of 5) for load development allows you to cover a wider range of variables with more resolution. That makes finding a good node easier, and still with acceptable confidence.
You can eke out a little more confidence by measuring each group twice- horizontally and vertically - and taking the average. This is a little dicey, though, because barrel vibrations tend to skew groups to the point where they aren't truly random. (They may string in one direction or another). At least in very accurate rifle they do. This effect gets drowned out by others with less accurate rifles.
And as they say, groups don't get smaller when you fire more shots. The odds of a big three shot group being an outlier are small (but real - which is why we want to confirm what we see), so you're probably just wasting ammo adding two more shots to a big three shot group.
The *best* way to measure groups is not to measure them at all, but to measure every shot. Take the standard deviation of each shot's distance from the center of the group and use that as a measure. There are phone/computer apps that will do this (or something similar), but it's not practical when your groups are one ragged hole.