Grouping explaination

I would like to know what are the parameters for grouping? I'm new to accuracy shooting, and I don't want to sound like a fool when I talk about how my rifle groups. How many shots does one need to take at a group to say a rifle is accurate 3,5,10? I was assuming 3 since I thought that was what the factory claimed their 1" at 100yrds addvertising with, is this correct or does their need to be more rounds then 3? How much time is taken between each round, is it click click boom, or do you wait a minute or two for the gun to cool down? When refering to groups past 3 rounds, could one assume that the accuracy will always suffer due to fouling and an unclean barrel? To some these questions may sound dumb, but please bear with me. I guess if one is looking for a factory rifle and the claims are that it shoots 3 rounds under an inch at 100yrds, could this be false advertising for a rifle they claim to have out of the box accuracy with since we don't know where that 4th and 5th etc. round ends up at? Just give me your thoughts, not looking for any brand name rifle explaination or put downs, just looking for a general definition of "grouping", and if you can please be technical meaning trying to stay away from general opinions and such. Thanks guys.