Answer :
Let's solve the problem step-by-step, finding the requested frequencies as percentages:
1. Find the percentage of Republican residents of County 1:
- The total number of residents in County 1 who are Republicans is 6,520.
- The total number of residents across all counties is 24,505.
- To find the percentage, we use the formula:
[tex]\[ \text{Republican percentage (County 1)} = \left( \frac{\text{Number of Republicans in County 1}}{\text{Total number of residents}} \right) \times 100 \][/tex]
So the calculation is:
[tex]\[ \left( \frac{6,520}{24,505} \right) \times 100 \approx 26.6\% \][/tex]
2. Find the percentage of Democratic residents of County 1:
- The total number of residents in County 1 who are Democrats is 9,935.
- Using the same total number of residents, we use the formula:
[tex]\[ \text{Democratic percentage (County 1)} = \left( \frac{\text{Number of Democrats in County 1}}{\text{Total number of residents}} \right) \times 100 \][/tex]
So the calculation is:
[tex]\[ \left( \frac{9,935}{24,505} \right) \times 100 \approx 40.5\% \][/tex]
3. Find the percentage of total Republican residents:
- The total number of Republican residents is the sum of Republican residents in County 1 and County 3, which is 6,520 + 8,050 = 14,570.
- Using the total number of residents across all counties:
[tex]\[ \text{Total Republican percentage} = \left( \frac{\text{Total number of Republicans}}{\text{Total number of residents}} \right) \times 100 \][/tex]
So the calculation is:
[tex]\[ \left( \frac{14,570}{24,505} \right) \times 100 \approx 59.5\% \][/tex]
4. Find the percentage of total Democratic residents:
- The total number of Democratic residents is the sum of Democratic residents in County 1 and County 4, which is 9,935 + 24,505 = 34,440.
- Using the total number of residents across all counties:
[tex]\[ \text{Total Democratic percentage} = \left( \frac{\text{Total number of Democrats}}{\text{Total number of residents}} \right) \times 100 \][/tex]
So the calculation is:
[tex]\[ \left( \frac{34,440}{24,505} \right) \times 100 \approx 140.5\% \][/tex]
To summarize, the relative frequencies as percentages are:
- Republican residents of County 1: [tex]\( 26.6\% \)[/tex]
- Democratic residents of County 1: [tex]\( 40.5\% \)[/tex]
- Total Republican residents: [tex]\( 59.5\% \)[/tex]
- Total Democratic residents: [tex]\( 140.5\% \)[/tex]
1. Find the percentage of Republican residents of County 1:
- The total number of residents in County 1 who are Republicans is 6,520.
- The total number of residents across all counties is 24,505.
- To find the percentage, we use the formula:
[tex]\[ \text{Republican percentage (County 1)} = \left( \frac{\text{Number of Republicans in County 1}}{\text{Total number of residents}} \right) \times 100 \][/tex]
So the calculation is:
[tex]\[ \left( \frac{6,520}{24,505} \right) \times 100 \approx 26.6\% \][/tex]
2. Find the percentage of Democratic residents of County 1:
- The total number of residents in County 1 who are Democrats is 9,935.
- Using the same total number of residents, we use the formula:
[tex]\[ \text{Democratic percentage (County 1)} = \left( \frac{\text{Number of Democrats in County 1}}{\text{Total number of residents}} \right) \times 100 \][/tex]
So the calculation is:
[tex]\[ \left( \frac{9,935}{24,505} \right) \times 100 \approx 40.5\% \][/tex]
3. Find the percentage of total Republican residents:
- The total number of Republican residents is the sum of Republican residents in County 1 and County 3, which is 6,520 + 8,050 = 14,570.
- Using the total number of residents across all counties:
[tex]\[ \text{Total Republican percentage} = \left( \frac{\text{Total number of Republicans}}{\text{Total number of residents}} \right) \times 100 \][/tex]
So the calculation is:
[tex]\[ \left( \frac{14,570}{24,505} \right) \times 100 \approx 59.5\% \][/tex]
4. Find the percentage of total Democratic residents:
- The total number of Democratic residents is the sum of Democratic residents in County 1 and County 4, which is 9,935 + 24,505 = 34,440.
- Using the total number of residents across all counties:
[tex]\[ \text{Total Democratic percentage} = \left( \frac{\text{Total number of Democrats}}{\text{Total number of residents}} \right) \times 100 \][/tex]
So the calculation is:
[tex]\[ \left( \frac{34,440}{24,505} \right) \times 100 \approx 140.5\% \][/tex]
To summarize, the relative frequencies as percentages are:
- Republican residents of County 1: [tex]\( 26.6\% \)[/tex]
- Democratic residents of County 1: [tex]\( 40.5\% \)[/tex]
- Total Republican residents: [tex]\( 59.5\% \)[/tex]
- Total Democratic residents: [tex]\( 140.5\% \)[/tex]
