Beware using averages -- if you can even find them.
Within every school the variation of scores is huge. At my school for instance, there is usually someone who fails substantially, someone around 270, and most scores in between. This is due to huge variation in motivation, study strategies, and (in my opinion) focus on understanding over memorization during the preclinical years between students.
In contrast, the variation between schools is not that great, and much of that variation can probably be explained by test-taking skills, intelligence (I realize that using this term on SDN is opening up a can of worms), and greater motivation for competitive specialties in the students it attracts, rather than factors intrinsic to the school itself.
I did very well but I think I could have scored within 5 pts of my score coming from any MD or DO school in the country.
Every accredited school will teach you nearly all the facts you need to ace the boards. Whether or not you do so depends on how hard you are willing to work for it.
I would be wary of schools with low pass rates however -- this may be indicative of a teaching problem.