The number of salespeople assigned to work during a shift is apportioned based on the average number of customers during that shift.  Apportion 16 salespeople using Webster's method given the information below.
Shift	Morning	Midday	Afternoon	Evening
Average number of customers	95	300	375	525
Salespeople to assign

What modified divisor did you use?

To apportion the 16 salespeople using **Webster's method**, we first need to determine the appropriate **modified divisor**. This divisor will allow us to distribute the salespeople proportionally to the number of customers in each shift.

### Steps:
1. **Total average customers**: Add the number of customers for all shifts.
   \[
   \text{Total customers} = 95 + 300 + 375 + 525 = 1295
   \]

2. **Calculate the initial divisor**:
   The total number of customers is divided by the number of salespeople available:
   \[
   \text{Initial divisor} = \frac{1295}{16} = 80.94
   \]
   This is the initial guess for the divisor. However, we'll need to modify this divisor to ensure we apportion exactly 16 salespeople.

3. **Assigning salespeople**:
   We now divide the average number of customers per shift by the divisor and round using Webster's method, which rounds **normally** (rounds down if below 0.5, rounds up if 0.5 or above):
   
   - Morning shift: \(\frac{95}{80.94} \approx 1.17 \) → 1 salesperson
   - Midday shift: \(\frac{300}{80.94} \approx 3.71 \) → 4 salespeople
   - Afternoon shift: \(\frac{375}{80.94} \approx 4.63 \) → 5 salespeople
   - Evening shift: \(\frac{525}{80.94} \approx 6.49 \) → 6 salespeople

   Adding these together: \(1 + 4 + 5 + 6 = 16\), which is the exact number of salespeople we needed to assign.

Thus, the **modified divisor** used is approximately **80.94**.

### Summary:
- The modified divisor used was **80.94**.
- Salespeople were assigned as follows:
  - Morning: 1 salesperson
  - Midday: 4 salespeople
  - Afternoon: 5 salespeople
  - Evening: 6 salespeople

Would you like more details on Webster’s method or any part of this process?

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Here are five related questions:
1. What is the difference between Webster's and Hamilton's method for apportionment?
2. How would the results differ if we used Jefferson’s method?
3. What happens if the divisor doesn’t yield an exact total of 16 salespeople?
4. Can Webster’s method ever result in a shift receiving zero salespeople?
5. How does the number of available salespeople affect the choice of the modified divisor?

**Tip:** Webster’s method uses rounding to the nearest integer, making it more balanced than some other apportionment methods that favor smaller or larger groups.

The number of salespeople assigned to work during a shift is apportioned based on the average number of customers during that shift. Apportion 16 salespeople using Webster's method given the information below. Shift Morning Midday Afternoon Evening Average number of customers 95 300 375 525 Salespeople to assign What modified divisor did you use?

Learn how to apportion 16 salespeople across shifts based on average customer numbers using Webster's method. This problem covers key concepts of apportionment, division, and rounding techniques, with a step-by-step explanation for calculating the modified divisor and assigning salespeople to shifts.

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