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Not really. Let's have 10 gunfights. 9 of them occur at 5 feet, 1 is at 155 feet. The average (your definition) distance in the fights is 20 feet, but 9 (90%) are inside the average while only one (10%) is outside. That is why the median is important for, as Glenn put it, understanding "actual distributional properties".
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These figures were the FBIs, so I dunno. I suspect there were a heck of a lot more than 10 gunfights david.
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Which points me toward yet another hypocritical practice. Putting bullets in a puny calibered carry gun. If your reason for making the choice to carry puny is based on the small probability of actually needing to fire the weapon it is hypocritical thinking to load that weapon. Is this incorrect.
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Something like what Jeff Cooper said about .25 autos and weither to keep them loaded or not. In fact, why not just use a plastic gun if most usages of guns never fire a round. Like I said, the rounds ability to stop some one is usefull if you really have to fight for your life. If one's not interested in that, sure carry a .22 or .25. Heck, carry a twinkie if twisted stats like those above are what you go for.