Every time I have heard the expression about someone being uneducated but having common sense I wonder at what point in the education process you start losing your common sense? I have never been sure why we would be born with common sense that starts to slowly disappear as we start the educational process. Probably the best segments of the Daily Show are the segments that Jordan Klepper does when he interviews Trump supporters at one of the Trump rallies. When Trump said he "loves the poorly educated" it explains how so many millions of people seem devoted to Trump.
One sign of intelligence is an awareness of how much you don't know and the sign of unintelligence is to overestimate what you know. One of the best studies on this point is the study done by Kruger and Dunning. This explains Trump and his supporters.