Suppose that a university has 39
 scholarships to be apportioned among 515
 English majors, 137
 psychology majors, and 536
 graphic design majors. Use the Jefferson method to determine how the scholarships should be apportioned among the three major groups.


To solve this problem using the **Jefferson method** of apportionment, follow these steps:

1. **Calculate the standard divisor (SD):**
   The standard divisor is the total number of students divided by the total number of scholarships.
   \[
   \text{SD} = \frac{\text{Total number of students}}{\text{Total number of scholarships}} = \frac{515 + 137 + 536}{39} = \frac{1188}{39} \approx 30.46
   \]

2. **Divide each group's population by the standard divisor:**
   For each major, calculate how many scholarships they would receive by dividing their population by the standard divisor. This gives us a preliminary idea of how many scholarships each group should get.

   - For English majors:
     \[
     \frac{515}{30.46} \approx 16.91
     \]
   - For Psychology majors:
     \[
     \frac{137}{30.46} \approx 4.50
     \]
   - For Graphic Design majors:
     \[
     \frac{536}{30.46} \approx 17.60
     \]

3. **Lower the divisors to whole numbers:**
   Since the Jefferson method lowers the divisor to give a whole number of scholarships, we begin by assigning each major the **whole number part** of the preliminary quota:

   - English majors: 16 scholarships
   - Psychology majors: 4 scholarships
   - Graphic Design majors: 17 scholarships

   Total so far = 16 + 4 + 17 = 37 scholarships assigned.

4. **Distribute the remaining scholarships:**
   We have \(39 - 37 = 2\) scholarships left to assign. According to the Jefferson method, assign the remaining scholarships based on the **largest fractional parts** from the previous step.

   - English majors: Fractional part = 0.91
   - Psychology majors: Fractional part = 0.50
   - Graphic Design majors: Fractional part = 0.60

   The largest fractional parts are:
   - English majors (0.91) and Graphic Design majors (0.60).

   These two groups will each receive one of the remaining scholarships.

5. **Final apportionment:**
   After distributing the remaining scholarships, the final apportionment is:

   - English majors: 16 + 1 = 17 scholarships
   - Psychology majors: 4 scholarships
   - Graphic Design majors: 17 + 1 = 18 scholarships

Thus, the final distribution of scholarships using the **Jefferson method** is:

- **English majors**: 17 scholarships
- **Psychology majors**: 4 scholarships
- **Graphic Design majors**: 18 scholarships

---

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How does the Jefferson method differ from the Hamilton method of apportionment?
2. Can the Jefferson method always guarantee a fair distribution?
3. How do you handle ties in fractional parts when using the Jefferson method?
4. What happens if the number of scholarships left is greater than the number of largest fractional parts?
5. What are the pros and cons of using the Jefferson method in real-world applications?

**Tip**: The Jefferson method tends to favor larger groups since it rounds down quotas and gives extra seats to those with the largest remainders.

Suppose that a university has 39 scholarships to be apportioned among 515 English majors, 137 psychology majors, and 536 graphic design majors. Use the Jefferson method to determine how the scholarships should be apportioned among the three major groups.

Learn how to distribute 39 scholarships among English, Psychology, and Graphic Design majors using the Jefferson method of apportionment. This step-by-step guide explains how to calculate the standard divisor and allocate resources fairly across three groups with a total of 1188 students.

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