The Sporcle website has a quiz for mapping the states of the United States. Sasha Trubetskoy posted a map of the results (or see the version with the state names) and along with it are the results (and the results are unscientifically confirmed by another online quiz):
Iowa is at the center of the main clump of least remembered states. But Iowa is also at the center of what most people think of as the Midwest. Apparently, the Heartland is terra incognita for most Americans. People fly over it in planes and in their minds, just some vague nowhere in the middle of the country.