Question

20. Four new teachers will be hired by a school district and apportioned to the six locations shown, based on the number of students at each location. Apply the Huntington-Hill method to determine how many new teachers (if any) each location should receive. Use the formula: HHN p2 n(n+1) Location A B С D E Number of Students 312 250 205 160 350 Current # of teachers 13 10 9 6 15 H-Hill Numbers (1) H-Hill Numbers (2) H-Hill Numbers (3) H-Hill Numbers (4) Final Apportionment

Answer 1

Given:

Steps:

1. Calculate Standard divisor = Total number of students/ (current # of teachers + New # of teachers)

2. Divide each location’s # of students with standard divisor to calculate quota

3. Lower down the quota to nearest integral value

4. Calculate geometric mean (GM) of Quota as Sqrt (n * n+1)

5. If GM > Quota, lower the Quota value or else upper round off the value and enter into Initial allocation column

6. Based on summation of initial allocation value, comparable to total number of teachers; reduce/ increase standard divisor value.

7. Iterate the process till initial allocation summation matches with total number of teachers.

Iteration 1:

Iteration 2:

Iteration 3:

Hence Final Allocation is as follows,

Location	Number of Students	Current # of teachers	New teachers	Total Teachers
A	312	13	1	14
B	250	10	1	11
C	205	9	0	9
D	160	6	1	7
E	350	15	1	16
				57

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