Properly used statistics are a very powerful tool. Just attacking the statistics won't get you very far, unless you can find error in their math.
The comments about "average" -- that's not statistics, that's basic math. The "average" voltage in your house is zero. It's a sine wave, and the "average" of a sine wave is zero. That doesn't mean that math/statistics are wrong, it means you don't have enough of an education in math to use the right tool for the job. With sinusoidal AC voltage we use "root-mean-square", average is meaningless.
The right tool for the job. Plus a lot of people here are using "statistics" to mean "gathered infromation". Statistics is not demographics. The murder rate is that, the documented historical rate that murders occur in our population.
Now looking at murder rate vs some other factor, say number of firearms or perhaps number of CCW permits, that can be done with the tools of statistics, BUT (and if this sentence means nothing to you, perhaps actually studying statistics would help) correlation does not equal causality. One more time, just because something is statistically correlated, does not mean you've found the (or a) cause for that something.
One thing that statistics as a tool help you do is rule out a hypothesis. Let's say I think that gun crimes are committed by people who watch Spongebob Squarepants. I interview those who have committed gun crime, and find out how many of them watch Spongebob. I'll probably be able to easily demonstrate mathematically that there is no correlation. But, what if there is? That still doesn't prove my hypothesis, and there are a number of alternative concepts that could explain the correlation.
What you need to focus on attacking would be the premise and conclusions.
It's like the Brady Bunch information on the number of "children" killed annually by firearms. Attack their premise -- their definition of "children". (Which I think includes those up to age 25?) Attack their conclusion "more gun laws would mean fewer gun crimes". Attacking their numbers, unless you have enough statistics classes under your belt to prove their math is in error, is grasping at straws.