Just because there's a higher crime rate there doesn't mean that each individual there is looking to mug you, though. (Football fans may be more prone to fistfights than baseball fans, but that doesn't mean that every football fan is going to beat you up — or that no baseball fan will do so.)
No, but I'd also expect that lower income areas would be more likely to mug someone in particular. You have to be pretty poor to be willing to attack someone for pocket change.
There's a lot of background mess in our mental pictures of the world. We try and be accurate on important issues, but a whole lot of the less important stuff we pick up from the media, the movies, and random impressions. And once these impressions are in our mental pictures, they just don't go away - until we find a fact that causes us to say "huh", and reassess.
Here are three facts that have caused that "huh" in me, recently, and completely rearranged minor parts of my mental map. I'm sharing them here, because that experience is a valuable one.