I have to do a problem where : a) Find the standard division d
b) Find the exact quotas for each of the republics
c) Find the apportionment of seats using Hamilton's method
The info is REPUBLIC: Argh Brwd Chrd Dstyr Eoia
Population:7.65 4.45 8.52 9.98 6.51
For A i got 0.74 is that correct?
For B) A: 10.337 B: 6
C I don't know what to do
To find the standard deviation (not division), you need to follow these steps:
Step 1: Calculate the mean (average) of the population numbers.
Step 2: Subtract the mean from each population number.
Step 3: Square the result of each subtraction.
Step 4: Calculate the average of the squared differences.
Step 5: Take the square root of the result from step 4.
Using the given population numbers of the republics (7.65, 4.45, 8.52, 9.98, 6.51), let's calculate the standard deviation:
Step 1: Mean = (7.65 + 4.45 + 8.52 + 9.98 + 6.51) / 5 = 36.11 / 5 = 7.222.
Step 2: Subtract the mean from each population number:
7.65 - 7.222 = 0.428.
4.45 - 7.222 = -2.772.
8.52 - 7.222 = 1.298.
9.98 - 7.222 = 2.758.
6.51 - 7.222 = -0.712.
Step 3: Square the result of each subtraction:
(0.428)^2 = 0.183184.
(-2.772)^2 = 7.686384.
(1.298)^2 = 1.683604.
(2.758)^2 = 7.612164.
(-0.712)^2 = 0.506944.
Step 4: Calculate the average of the squared differences:
(0.183184 + 7.686384 + 1.683604 + 7.612164 + 0.506944) / 5 = 17.67228 / 5 = 3.534456.
Step 5: Take the square root of the result from step 4:
Square root of 3.534456 ≈ 1.88.
So, the standard deviation (d) is approximately 1.88.
Now, let's move on to finding the exact quotas for each of the republics.
To find the exact quotas, divide each republic's population by the standard deviation (d).
Republic A: 7.65 / 1.88 ≈ 4.08 (approximate quotient).
Republic B: 4.45 / 1.88 ≈ 2.36 (approximate quotient).
Republic C: 8.52 / 1.88 ≈ 4.53 (approximate quotient).
Republic D: 9.98 / 1.88 ≈ 5.31 (approximate quotient).
Republic E: 6.51 / 1.88 ≈ 3.47 (approximate quotient).
Now, let's move on to finding the apportionment of seats using Hamilton's method.
Hamilton's method for apportionment involves taking the truncated quotas (integers) of each republic and distributing any remaining seats based on the largest remainders. The republic with the largest remainder receives each remaining seat until all seats are allocated.
Using the truncated quotas:
Republic A: 4 (truncated quotient).
Republic B: 2 (truncated quotient).
Republic C: 4 (truncated quotient).
Republic D: 5 (truncated quotient).
Republic E: 3 (truncated quotient).
Now, we have 19 seats allocated (4 + 2 + 4 + 5 + 3).
To allocate the remaining seat, we will compare the decimal part (remainder) of each quotient and award the remaining seat to the republic with the largest decimal part. If decimal parts are tied, award the seat to the republic with the largest original population.
The decimal parts for each republic are as follows:
Republic A: 4.08 - 4 = 0.08.
Republic B: 2.36 - 2 = 0.36.
Republic C: 4.53 - 4 = 0.53.
Republic D: 5.31 - 5 = 0.31.
Republic E: 3.47 - 3 = 0.47.
Since 0.53 is the largest decimal part, the remaining seat goes to Republic C.
Therefore, the apportionment of seats using Hamilton's method is as follows:
Republic A: 4 seats.
Republic B: 2 seats.
Republic C: 5 seats.
Republic D: 5 seats.
Republic E: 3 seats.
I hope this helps! Let me know if you have any further questions.
To find the answers to parts (a), (b), and (c) of your problem, we need to understand the concepts of standard division, exact quotas, and Hamilton's method for apportionment.
a) Standard Division (d):
The standard division is a measure used to allocate seats in proportion to the population of each republic. It is calculated by dividing the total population by the total number of seats. In this case, the total population is the sum of the populations of all republics.
To find the standard division (d):
1. Add up the populations of all the republics: 7.65 + 4.45 + 8.52 + 9.98 + 6.51 = 37.11.
2. Divide the total population by the total number of seats to get the standard division: d = 37.11 / (number of seats).
You did not mention the number of seats, so I will assume it's not given. Please provide the number of seats to calculate the correct standard division (d).
b) Exact Quotas for Each Republic:
The exact quota for each republic represents the number of seats each republic would receive if the number of seats allocated were solely based on its population, without any rounding or adjustment.
To find the exact quota for each republic:
1. Divide the population of each republic by the standard division (d).
- For Argh: 7.65 / d
- For Brwd: 4.45 / d
- For Chrd: 8.52 / d
- For Dstyr: 9.98 / d
- For Eoia: 6.51 / d
You provided the values for A (10.337) and B (6), but without the actual standard division (d), it is not possible to confirm if they are correct. Please provide the correct standard division to calculate the exact quotas accurately.
c) Apportionment of Seats using Hamilton's Method:
Hamilton's method is a procedure used for apportionment. It involves the following steps:
1. Calculate the initial quotas (exact quotas) for each republic based on its population, as we did in part (b).
2. Assign one seat to each republic (floor the exact quotas).
3. Distribute any remaining seats among the republics that have the largest fractions in their quotas until all seats are allocated.
To apply Hamilton's method:
1. Calculate the exact quotas for each republic.
2. Assign one seat to each republic (round down the exact quotas).
3. Determine the remaining seats by comparing the fractional parts left after rounding down each republic's quota.
4. Distribute the remaining seats based on the highest fractional parts until all seats are allocated.
Please provide the correct standard division (d) so that we can proceed with calculating the exact quotas accurately and then proceed to Hamilton's method for apportionment.