My trouble is that more often than not, we are basing our stereotypes on inaccurate information, so therefore not really making ourself more safe by heeding the ones that are trying to warn us.
For instance, if two out of three beaches contain man eating sharks on the east coast does that really indicate that east coast beaches are bad? More often than not, the reality of the example is that one of dangerous beaches was in South Carolina and the other one was in Florida. So if I'm going to go swimming off the coast of Maine, should I use those other two examples as a distinct possibility that I'll get eaten by sharks? Not if I'm a reasonable person.
That's the danger with confusing correlation and causation. More often than not, we base our stereotypes on false correlations as if they are causal. This is why most stereotypes are inaccurate. You are not more likely to be eaten by a shark on an east coast beach. You're more likely to be eaten by a shark on a beach that's on warm water. So if I decide to go swimming off the coast of Australia and deem it safe because it's not one of those horrible east coast man eating shark beaches, I might be surprised when a shark comes to eat me. Here's a case where stereotyping does nothing to make you safer and is based on correlating the wrong information.
This is also something we do often with regards to race. In the US, you are more likely to raped and assaulted by a white person than by a black person. Yet it is the black people we decided to avoid and walk on the other side of the street when they pass. We are making correlations based on inaccurate racial stereotypes. Comparing a group of people dressed in gangsta wear to old ladies seems a bit of a stretch for me because the information you're getting about one group (the old ladies) is more accurate than the info you're getting from the other. It would not be unreasonable to assume that if a gang of old ladies attacked you, you could probably take them or outrun them. So it's not unreasonable to dismiss any threat.
But if you're feeling defensive when a group of young guys in gangsta gear approach (in this situation those young men could be white, I don't know...but usually when one says gangsta gear, they are referring to black people, so please correct me if I am wrong), what is the information you're basing that threat on? Personal experience of being attacked by such? Most of the time, we develop our perceptions of such people based upon how they are portrayed to us in the media, and that is usually heavily weighted on the crime side. The actual statistics show that you are far less likely to be attacked by such a gang then by white people though.
Unfortunately, that type of stereotyping has lead to things such as racial profiling by police.
Having lived in the same neighborhood and having been the teacher of a whole lotta young guys who sport gansta gear, I can't say that they are any more likely to cause me trouble on the street than some young guys in ties. I can draw other conclusions, such as the young guys in ties are likely going to the type of job that requires a tie and the guys in gansta gear are probably not heading to such a job, but anything beyond that would be hard to base on accurate information.
When I call a stereotype into question, you'll note that I almost always qualify that with the words inaccurate or harmful or both. Stereotyping is something we do when we don't have enough information and more often than not ends up being based on the wrong information or not enough information. It may appear that such stereotyping creates a positive outcome, but the reality usually reflects something different than that.