Suppose that an achievement test in mathematics was given to students from two different high schools A and B. When the results of the test were tabulated, it was found that the average score for the freshmen at school A was higher than the average for the freshmen at school B, and that the same relationship existed for the sophomores, the juniors, and the seniors at the two schools. On the other hand, it was found also that the average score of all the students at school A was lower than that of all the students at school B. Discuss and explain these results. Give an example of how this could happen.