I once read a very interesting murder mystery in which a profiler started spouting the typical characteristics of a serial killer and another character pointed out that given the number of crimes that go unsolved that these characteristics really represented the profile of people who were caught, not serial killers as a whole.
But we do tend to look for ways to narrow our searches (in fiction and in real life, with crime and with other things) and so statistics and probabilities often come into play. And many times, in my fictional crime reading have I come across the so-called statistic that women are more likely to use poison. Except, it turns out its not true.