Question

The following table shows the number of fifth and sixth grade teachers in a school district and the number of students in each of those grades. The number of teachers for each of the grade levels was determined by using the Huntington-Hill apportionment method. The district has decided to hire a new teacher for either the fifth or sixth grade.

	Number of teachers	Number of students
Fifth grade	19	607
Sixth grade	23	739

(a) Use the apportionment principle to determine to which grade the new teacher should be assigned.  

(b) Use the Huntington-Hill apportionment principle to determine to which grade the new teacher should be assigned.

How does this result compare with the result in part (a)?

same result or different result

Answer 1

Given : The following table shows the number of fifth and sixth grade teachers in a school district and the number of students in each of those grades.

a. First find out the average constituency to calculate absolute unfairness which decide which grade the new teacher should be assigned,

	Number ofTeachers	number of students	Average Consitituency
Fifth Grade	19	607	607/19 = 32
Sixth grade	23	739	739/23 = 32

Since , we have to calculate new average constituency consider that one teacher increases in every grade, therefore

	Number ofTeachers	number of students	Average Consitituency(new)
Fifth Grade	20	607	607/20=32
Sixth grade	21	739	739/22=33

Comapre the average constituency of both grade

	Average Consitituency(old)	Average Consitituency(new)
Fifth Grade	32	32
Sixth grade	32	33

Now we calculate absolute unfairness

	Fifth Grade Average Constituency	Sixth Grade Average Constituency	Absolute unfairness of apportionment
Fifth Grade receives new Teacher	32	31	32-31=1
Sixth grade receives new Teacher	32	33	33-32=1

Hence , as we seen in above table fifth grade absolute anfarimess is 2 and sixth grade absolute unfairness is 1, therefore sixth grade will recevice a new teacher.

b.In Hunting hill method first we calculate the district size , formula for district size is

Therefore

Now calculate state quota by dividing each grade student by D

	Number of teachers	Number of students	State Quota	n	n +1	Geometric Mean	Teachers
fifth grade	19	609		18	19		19
Sixth grade	23	739		21	23		23

hence, there is a loss of one teacher from Sixth grade from 22 to 21, therefore new teacher will be added to sixth grade.

the part b is same as part a beacuse in both parts new teacher will be added to sixth grade.