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<p>This shows another problem with looking at aggregate data. Simpson’s Paradox could be at work here. For instance, it could be that males and females do equally well in each class, but females are more likely to take classes in which grades are higher. A trivial example would have two classes. In class A, there are eight females and two males, and everyone gets an A. In class B, there are two females and eight males, and everyone gets a B. Females have an average GPA of (32+6)/10 = 3.8 while males have (8+24)/10 = 3.2. It is absolutely possible that the students in class A really are better, but we cannot say for sure without more information.</p>