Lots of articles and books put forward the number 2.7, so there must be some good statistical data behind that number, but that doesn't mean much.
My understanding is that the meme that "most gunfights have 3 shots fired" comes from the old NYPC SOP 9 reports.
The NYPD records and tracks data on every officer involved shooting and publishes a report each year. These shootings include fights with criminals, accidental discharges, and suicides.
This info has been circulating in the LEO community for years. If you do some very simple statistical analysis of older SOP 9 reports I think you'll see the origin of the belief that "less then 3 rounds are rifed in most gunfights."
Personally, I think the SOP is widely and wildy misinterperated and that maxim on the law number of shots fired should be regarded as basically an urban myth at this point.
When the NYPD carried six shot revolvers, which was until fairly recently, the average number of rounds fired by NYPD officer in a fight was almost always six or less. When you add in the number of AD's and suicides (where presumbly only one round is fired) and then average the result, the number of "rounds fired per incident" (not fight, but incident, which is what they tracked) would skew even lower.
Now that the NYPD has been carrying Glocks for awhile, my understanding is the average number of rounds fired per actual "gun fight" has gone up. Basically, when they carried a six shot revovler, they fired up to six. Now that they have a 15 (or more) round Glock, they shoot more.
I don't have the documentation to back this up. This is just my understanding based on the reading I've done and what other people with better info than I have said on the subject.
So, the take away is, don't believe the old "most gunfights involve less then 3 rounds" story.