Here's something interesting from a New York Times poll a couple weeks ago. People were asked what percentage of all Americans are black. Results include that 8 percent of whites, and 17 percent of blacks, guessed that more than 50 percent of all Americans are black. (It's question 80 in the poll.)
The actual figure, from the 2006 census estimates, is 12.4 percent. (If you had asked me, I would have probably said twelve percent, which is the figure I learned quite some time ago.)
Jordan Ellenberg, who linked to this poll, asks whether people are ignorant of what "50 percent" means, or whether they're ignorant of the actual makeup of the United States population. I'm not sure how to answer this.
But I'd be interested to know how people's guesses of the percentage of the population which is black are correlated with the percentage of the population in their immediate area which is black. People probably expect that the people around them are representative of the general population, because psychologically we may be wired that way; numbers, even numbers obtained from counting millions of people, just don't have the same psychological impact as the faces you see while walking down the street. (You might have to factor in some other things, though, such as people's choice of television shows, movies, etc.; subconsciously we might not be that good at distinguishing between people that we're seeing on television and people we're seeing in reality.)
Similar questions could be asked in other populations. For example, if you ask Philadelphians about the racial distribution of Philadelphia, what do they say? For black and white people, the answer is 44.3% black, 41.8% white, from this Census Bureau page with a ridiculously long URL. But most Philadelphians live in neighborhoods that are mostly black or mostly white, so I suspect you'd get a lot of extreme answers.
Although the extreme answers might not correspond to what people actually see day to day! There may be people living in mostly-white neighborhoods who think most Philadelphians are white, or people living in mostly-black neighborhoods who think most Philadelphians are black. But you might also see people living in mostly-white neighborhoods who feel like their neighborhood is one of the only places where white people live, and guess that the city is mostly black, or vice versa. (Note to people who know anything about Philadelphia -- I am not saying that such neighborhoods exist, or that I know which ones they are. I'm just saying I can imagine them.)
Yes, in my secret other life I want to study things like that.