Class size and departments. A university classifies its classes as either “small” (fewer than 40 students) or “large.”

A dean sees that 62% of Department A’s classes are small, while Department B has only 40% small classes. She wonders if she should cut Department A’s budget and insist on larger classes. Department A responds to the dean by pointing out that classes for third- and fourth-year students tend to be smaller than classes for first- and second-year students. The three-way table below gives the counts of classes by department, size, and student audience. Write a short report for the dean that summarizes these data. Start by computing the percents of small classes in the two departments, and include other numerical and graphical comparisons as needed. (Do not perform any statistical significance tests.) Here are the numbers of classes to be analyzed:

Department A Department B Year Large Small Total Large Small Total First 2 0 2 18 2 20 Second 9 1 10 40 10 50 Third 5 15 20 4 16 20 Fourth 4 16 20 2 14 16