Thanks for that Zebrahat! So it would appear to me, based on the information that Zebrahat provided, that the search volume doesn't dictate competition, at least not directly. The number of pages that Google returns, plus the pages that have the keywords actually embedded in them, dictates competition.
Thus, a low search volume keyword that returns thousands of pages, with hundreds of pages optimized for that keyword, is much more competitive than a high search volume keyword with just a few dozen pages, that have no on page optimization at all.