EXAMPLE 16 Apportioning Classes by the Webster Method

Let us return to the case of the mathematics teacher who is to teach a total of five classes in geometry, precalculus, and calculus. The enrollments are 52 for geometry, 33 for precalculus, and 15 for calculus. With a total of 100 students enrolled, and a house size of 5, the standard divisor is 20. The quotas, determined by dividing the enrollments for the three subjects by the standard divisor, are 2.60, 1.65, and 0.75, respectively. The tentative apportionments are 3, 2, and 1; their total, 6, exceeds the house size. We therefore will try a divisor greater than 20. using 21 as the divisor, we find that the apportionment quotients are 2.48 for geometry, 1.57 for precalculus, and 0.71 for calculus. Rounded, these quotients become 2, 2, and 1, respectively, for a total of 5 classes. Thus, geometry and precalculus are each apportioned 2 classes, and calculus gets 1 class. This is the same apportionment that we obtained with the Hamilton method.