Forget what you were taught about this in school. Research current publications on violence linked to genetics. Keep an open mind while you do this, understanding that every possible effort has been expended by those who would like to deny this linkage.
Yes, there is a link between low IQ and crime. There is also evidence that much can be overcome with culture.
Crime rates could be brought down significantly if respect for the rule of law was taught and believed by all.
Lots of reasons that it is not. Genetics does not rule all when it comes to crime.
You have probably read The Bell Curve. It gives some useful suggestions.
The Middle ages data is not pushed in current education, but it does show that when you have little respect for the rule of law, homicide rates soar.
I am not disputing a statistical link of low IQ to crime. I am saying that respect for the law can be taught to low IQ individuals. There is also evidence that IQ is partially cultural, and can be raised some amount.