I don't think that medical schools make their average board scores public anymore. You might want to go to the Medical Students board and ask any of them if they know their individual school's average.
I'm not sure it's that useful of a statistic, to be honest. It's a standardized test, so if you did well on the MCAT, you'll do well on the boards. In essence, looking at board scores is going to be similar when looking at MCAT scores for a school. It will tell you a lot about the people who go to a school, but it won't tell you much about the school itself.
I am sure that there is an MCAT/Boards correlation, but some schools consistently have much higher Boards averages than MCAT. UF, for example, has average MCAT scores (30ish), but had ~227 Step I average this year. I might be a little biased, but I think that this does indeed say something about the school itself.
