@ Slipstick, the actually accuracy of the numbers isn't what Greg is asking about. He wants to know the proper textual interpretation of that particular paragraph.
Greg,
Both of those answers are incorrect. The second answer is blatantly wrong because the second method of calculation, which clearly doesn't agree with the first, doesn't place an upper limit, no less one of 3 million. You can combine separate methods of calculation into one combined answer. And citing the majority result as "the summary" of the paragraph would be incorrect as well, since the minority result is listed, and some controversy is mentioned. What it doesn't say is what the source of that controversy is. Is it how to apply the maths? Which type of events should count as a defensive shooting?
In fact, I would suggest that the context of that statement matters a great deal in interpreting the "on the other hand". For instance, let's say the document is from an anti-gun website, and the subsequent paragraph says something like "However, when inspecting these two methods, removing cases of more than one gunshot per encounter, etc etc, the numbers align far more towards the 108,000 figure, thus demonstrating that gun enthusiasts will encourage inflated numbers of defensive gun uses." Not saying that's what the study is meant to show, but if for instance that was the next paragraph, my reading of the one you cite would be:
1. Despite the apparently very high numbers of defensive gun uses, which some estimate to be as high as 3 million per year, other methods (which we will subsequently show to be more honest) show a far lower amount of incidents, closer to 108,000.
After all, why mention that the vast majority all agree with 500,000 - 3 million, and then cite a very different number, if the reason for the discrepancy isn't going to be addressed? Or maybe this would have been the next paragraph (and hence the conclusion):
2. This demonstrates that results in the 'social sciences' are often untrustworthy and can be greatly skewed depending on who's presenting the data and how they obtain their numbers.
Or maybe it's saying something about the field itself in terms of conformity to methods, in which case it might say this:
3. This demonstrates that since a few independent researchers achieves a wildly lower result, that the majority must all be employing the same method as each other. We can see from this that the majority of research consists of copying orthodox methodology with the same set of assumptions, which naturally will lead to similar results.
There are so many other possible interpretations. But I know what you were getting at, Greg, and if you don't want to look at other context then this is what you'd have to conclude:
1. The estimated range is most likely 500,000 to 3 million, with the small possibility that this number is inflated due to methodological error.