A popular one is comparing the violence in cities by their raw numbers instead of per-capita.

Whenever someone mentions raw numbers alarm bells go off in my head and I immediately assume there's some agenda. This should be normal, especially when people do such atrocious comparisons like x events in America vs y events in Iceland. Yet we see it done all the time.

I remember learning this in both high school physics and high school chemistry for unit conversions.

Sometimes you cannot directly compare two numbers because they are on two different scales. It is basically like saying 10cm is bigger than 5in because there are 10, ignoring the fact that if you normalized the values, 5in would be a larger distance.

Of course, it is usually never as obvious to the casual observer as using inconsistent units of linear distance.

Worse than this, sometimes you can't even compare numbers on the same scale. Inherit assumptions make things difficult to compare. For example: some event may depend highly on the interconnectedness (maximal clique in a graph) than population and this a per capita comparison isn't relevant.

But this is much more than statistics, this is understanding measurements and events. This is really the fundamental problem here, not a lack of understanding statistics (though good statisticians are experts in asking these types of questions).

You might be amused my this -- Limmy on feathers and steel.

https://www.youtube.com/watch?v=-fC2oke5MFg

Not sure why I couldn't find it on his channel. https://www.youtube.com/c/LimmyLimond/