Question

Suppose that a university has 31 scholarships to be apportioned among 279 English majors, 215 psychology majors, and 597 graphic design majors. Use the Jefferson method to determine how the scholarships should be apportioned among the three major groups.

Answer 1

Explanation:

Calculate the initial quotas for each group by dividing the number of scholarships (31) by the number of individuals in each group:

English majors: 31 scholarships / 279 students ≈ 0.111 scholarships per student.

Psychology majors: 31 scholarships / 215 students ≈ 0.144 scholarships per student.

Graphic design majors: 31 scholarships / 597 students ≈ 0.052 scholarships per student.

For each group, separate the initial quotas into whole numbers and remainders:

English majors: 0 scholarships per student with a remainder of 0.111.

Psychology majors: 0 scholarships per student with a remainder of 0.144.

Graphic design majors: 0 scholarships per student with a remainder of 0.052.

Sort the groups by their remainders in descending order:

Psychology majors (0.144)

English majors (0.111)

Graphic design majors (0.052)

Allocate one scholarship to each group based on their whole numbers:

English majors: 0 scholarships + 1 scholarship = 1 scholarship.

Psychology majors: 0 scholarships + 1 scholarship = 1 scholarship.

Graphic design majors: 0 scholarships + 1 scholarship = 1 scholarship.

Now, recompute the quotas for each group based on the remaining scholarships (28) and their remainders:

English majors: 28 scholarships / 279 students ≈ 0.100 scholarships per student.

Psychology majors: 28 scholarships / 215 students ≈ 0.130 scholarships per student.

Graphic design majors: 28 scholarships / 597 students ≈ 0.047 scholarships per student.

Again, sort the groups by their new quotas in descending order:

Psychology majors (0.130)

English majors (0.100)

Graphic design majors (0.047)

Allocate the remaining scholarships based on their whole numbers:

English majors: 1 scholarship + 10 scholarships = 11 scholarships.

Psychology majors: 1 scholarship + 13 scholarships = 14 scholarships.

Graphic design majors: 1 scholarship + 4 scholarships = 5 scholarships.

So, using the Jefferson method, the scholarships should be apportioned as follows:

English majors: 11 scholarships

Psychology majors: 14 scholarships

Graphic design majors: 5 scholarships