In some cases this is true, but the associate between income and crime rate is not hard and fast, and people often overestimate it. Plus, people will often mistake "concentration of racial minorities" for "unsafe."
The book I just finished discusses a particular community where the geographical divide of a particular street also has functioned for decades as a racial divide, and people on the white side continue to believe that the black side is "the bad part of town," and avoid it as dangerous, with businesses even refusing to deliver there, when crime statistics fail to bear out that it's any more dangerous. In fact, there is a dangerous part of town, where crime rates are particularly elevated, but it's only a small part of the alleged dangerous part of town.
Is there a term for the way biases persist because the cost of updating them seems high compared to the cost of maintaining the bias?
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.