By mentioning certain remotely related facts, it looks as if you're hinting at giving an interpretation of the central facts.
If you want to convey facts about a topic like gun violence in Chicago, then stick to facts closely relevant to it. Like different ways of slicing up the data. You might show a density map of where in Chicago most of it has happened over a certain period, or demographics about gun violence.
Now if you want to explore a link between gun violence and something else like poverty, then you have to get your ducks in a row about that. Such a subject deserves to be treated by a sophisticated researcher with an expert background in statistics. If that researcher postulates some kind of link, they have to look at all the reasons why that might be false, not only true.
If you want to preempt those accusations of bias, then you need to cover your bases and present all the facts that the public may believe to be relevant. Even those facts which you personally believe to be irrelevant distractions from the narrative you prefer.
That's not the same as avoiding biases.
You can't pander to both at the same time. What you can do, and typically is done, is pander to one or the other by conforming to one narrative or the other, choosing or omitting facts according to the needs of one narrative or the other. That is pandering.