No, it's not "simple math" it's "simple bigotry." Perhaps an argument can be made that all humans are predisposed to bigotry in some form? Maybe we all suffer from this, and there isn't anything we can do about it, as it's a part of being human? As individuals, we have our own individual preferences, and therefore, we are prejudiced against the things that aren't preferred, to some degree.
From a purely pragmatic standpoint, I would venture to say less than 1% of southerners are in-bred, breathe through their mouth, never shower, and lack basic education. And this statistic is probably not much different nationwide, 'stupid' doesn't have boundaries. Nevertheless, it is a stereotype you have applied to a large group of people, based on ignorant bigoted prejudice. It's really no different than saying 'blacks are less intelligent than whites' or 'women are less qualified than men', as it uses the same bigoted stereotypical viewpoint and mindset. If you are willing to do this with Southerners, you are just as likely to do this with any number of other groups of people, yet we are all individual.
Sums up your entire supposition; Well done!