I this context I think you then need to separate stereotypes from risk factors. The problem with stereotypes is when you apply a statistical correlation of a trait of populations to an individual, rather than a risk assessment of that individual. It is true that statistically men are stronger than women, but if you go by stereotype and refuse to accept women's applications for a job requiring strength, you are making an error.
Even a statistical trait needs to be validated in a given individual. In your case, you've validated based on clothing and the racial component is merely an added factor, not the factor.
However, we also need to be clear on what statistics and correlation mean, and it appears to me you've made several errors including inverting the statistics.
Media narratives are not statistical. I don't even mean they have personal biases; it is simpler than that. We humans bias towards paying attention to outliers, not the statistical norm. There is no value in wasting cognitive effort to pay close attention to normal daily things. Natural selection has made sure that we eliminate such waste. It is when something unusual happens that we pay attention and remember. That's what makes something newsworthy. What you see in the media is not statistically representative; it is outliers. Perhaps more importantly, the news and the narratives don't give you the correct formation of the statistics. If you are walking down the street and see somebody with a certain appearance, what you want to know is, Given this appearance, what is the probability that they will attack me. The probability you provide is the inverse, Given that somebody is an attacker, what is the probability of them appearing like the people in front of me.
This is a very important distinction, because the two formulations are not directly related. 100% of crows are birds, but only a tiny % of birds are crows. The percent of crows that are birds stays the same at 100% all the time. The percent of birds that are crows varies all the time based both on intrinsic properties (number of crows existing) and extrinsic properties (number of non-crow birds existing).
In that context, it might be that the odds of those blacks in hoodies could be less likely to attack you than the white men in suits across the street. Let's take a quick look at how. Suppose there are 1000 black people and 40 of them are violent, and there are 500 white people and 30 of them are violent. Here's the math:
There are 70 violent people, of which 40 (57%) are black. Hence, *given that a person is violent, the odds are higher than they are black than white. This is the sort of narrative you might get from media exposure.
The odds that a black person is violent is 4% (40 of 1000). The odds that a white person is violent is 6% (30 of 500). This means, if you see a white person walking down the street they are 1.5 times more likely to attack you than if it is a black person (6% vs 4%).
Overall there is only a 4.67% chance of anyone attacking you (70 of 1500).
Do you see the difference? Now I'm not suggesting this is the case; but just be clear on the difference between the two formulations of probability: "Given X is true, what are the odds they are Y" vs "Given they are Y, what are the odds X is true?"
In reality there are more white people than black people, so you might say this is backwards. True, but that also means that, if you are going to be attacked, your attacker may more likely be white even if a blacks have a higher rate within their population. You really need to formulate the question properly and look up the correct demographics and statistics to answer that specific question. It's not as straightforward as people think. I hope that helps.
TL;DR: Validation is an important factor, which you seem to have. However, I think you have inverted the probability. source