A total of 25 teacher aides are to be apportioned among seven classes at a new elementary school. The enrollment in each of the seven classes is shown in the following table. Class Number of students Kindergarten 38 First grade 39 Second grade 35 Third grade 27 Fourth grade 21 Fifth grade 31 Sixth grade 33 Total 224 (a) Determine the standard divisor. What is the meaning of the standard divisor in the context of this exercise? There is one aide for every students. (b) Use the Hamilton method to determine the number of teacher aides to be apportioned to each class. Class Hamilton method Kindergarten First grade Second grade Third grade Fourth grade Fifth grade Sixth grade (c) Use the Jefferson method to determine the number of teacher aides to be apportioned to each class. Class Jefferson method Kindergarten First grade Second grade Third grade Fourth grade Fifth grade Sixth grade Is this apportionment in violation of the quota rule? YesNo (d) How do the apportionment results produced using the Jefferson method compare with the results produced using the Hamilton method? They are identical.Using the Jefferson method, the second grade gets one more teacher's aide and the third grade gets one less aide when compared to the Hamilton method. Using the Jefferson method, the fifth grade gets one more teacher's aide and the second grade gets one less aide when compared to the Hamilton method.Using the Jefferson method, the sixth grade gets one more teacher's aide and the fourth grade gets one less aide when compared to the Hamilton method.Using the Jefferson method, the first grade gets one more teacher's aide and the fifth grade gets one less aide when compared to the Hamilton method.
A total of 25 teacher aides are to be apportioned among seven classes at a new elementary school. The enrollment in each of the seven classes is shown in the following table. Class Number of students Kindergarten 38 First grade 39 Second grade 35 Third grade 27 Fourth grade 21 Fifth grade 31 Sixth grade 33 Total 224 (a) Determine the standard divisor. What is the meaning of the standard divisor in the context of this exercise? There is one aide for every students. (b) Use the Hamilton method to determine the number of teacher aides to be apportioned to each class. Class Hamilton method Kindergarten First grade Second grade Third grade Fourth grade Fifth grade Sixth grade (c) Use the Jefferson method to determine the number of teacher aides to be apportioned to each class. Class Jefferson method Kindergarten First grade Second grade Third grade Fourth grade Fifth grade Sixth grade Is this apportionment in violation of the quota rule? YesNo (d) How do the apportionment results produced using the Jefferson method compare with the results produced using the Hamilton method? They are identical.Using the Jefferson method, the second grade gets one more teacher's aide and the third grade gets one less aide when compared to the Hamilton method. Using the Jefferson method, the fifth grade gets one more teacher's aide and the second grade gets one less aide when compared to the Hamilton method.Using the Jefferson method, the sixth grade gets one more teacher's aide and the fourth grade gets one less aide when compared to the Hamilton method.Using the Jefferson method, the first grade gets one more teacher's aide and the fifth grade gets one less aide when compared to the Hamilton method.
Chapter9: Sequences, Probability And Counting Theory
Section: Chapter Questions
Problem 18PT: To allocate annual bonuses, a manager must choose his top four employees and rank them first to...
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A total of 25 teacher aides are to be apportioned among seven classes at a new elementary school. The enrollment in each of the seven classes is shown in the following table.
Class | Number of students |
---|---|
Kindergarten | 38 |
First grade | 39 |
Second grade | 35 |
Third grade | 27 |
Fourth grade | 21 |
Fifth grade | 31 |
Sixth grade | 33 |
Total | 224 |
(a) Determine the standard divisor.
What is the meaning of the standard divisor in the context of this exercise?
(b) Use the Hamilton method to determine the number of teacher aides to be apportioned to each class.
(c) Use the Jefferson method to determine the number of teacher aides to be apportioned to each class.
Is this apportionment in violation of the quota rule?
(d) How do the apportionment results produced using the Jefferson method compare with the results produced using the Hamilton method?
What is the meaning of the standard divisor in the context of this exercise?
There is one aide for every students.
(b) Use the Hamilton method to determine the number of teacher aides to be apportioned to each class.
Class | Hamilton method |
---|---|
Kindergarten | |
First grade | |
Second grade | |
Third grade | |
Fourth grade | |
Fifth grade | |
Sixth grade |
(c) Use the Jefferson method to determine the number of teacher aides to be apportioned to each class.
Class | Jefferson method |
---|---|
Kindergarten | |
First grade | |
Second grade | |
Third grade | |
Fourth grade | |
Fifth grade | |
Sixth grade |
YesNo
(d) How do the apportionment results produced using the Jefferson method compare with the results produced using the Hamilton method?
They are identical.Using the Jefferson method, the second grade gets one more teacher's aide and the third grade gets one less aide when compared to the Hamilton method. Using the Jefferson method, the fifth grade gets one more teacher's aide and the second grade gets one less aide when compared to the Hamilton method.Using the Jefferson method, the sixth grade gets one more teacher's aide and the fourth grade gets one less aide when compared to the Hamilton method.Using the Jefferson method, the first grade gets one more teacher's aide and the fifth grade gets one less aide when compared to the Hamilton method.
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