<p>except, mw, if you took a look at NUs sports program, and why it sucks so much, and talk to any of the athletes and people who pay attention to teh athletics there, NU compromises its academics for athletics to a much less degree than stanford or duke even. which means that not all top athletes have a chance at going to NU, which means your little anectdote about the 1220s just isnt true. </p>
<p>The one football player i met at NU was a Bill Gate’s Millenium scholar (bill gates chooses a handful of black kids and gives them all the money tehy need for colelge because they are so exceptional) and had a better SAT score than I do. lets not make generalizations. </p>
<p>Now, as for that terrible statistical analysis. If you report the IQR as 1320-1500, that means that 25% of the student body has above a 1500. It doesnt tell you whether they all got 1600s or all got 1510s, but eitehr is possible (if however unlikely in this case) and similarly, 25% of people got below a 1320. They could all have 800s, for all we know.
You cant make assumptions about the shape of a distribution based on the IQR. I think what you are trying to do is assume a normal distrubution (which is okay because we have such a large population sample) and use that to say that the mean should fall exactly halfway between teh 25th adn 75th percentile. </p>
<p>As your own analysis shows, the assumption of normality didnt work out too well. Its very possible that the mean does not fall halfway between, because its very possible that the distribution isnt normal.</p>