Residents of three counties were polled to find the percentage of residents who are Republican or Democrat.
| | Democrat | Republican | Total |
| :------ | :------- | :--------- | :---- |
| County 1 | 4,050 | 2,470 | 6,520 |
| County 2 | 3,925 | 6,010 | 9,935 |
| County 3 | 2,100 | 5,950 | 8,050 |
| Total | 10,075 | 14,430 | 24,505|
Find the following relative frequencies to the nearest tenth of a percent.
Republican residents of County 1: $\square$ %
Democratic residents of County 1: $\square$ %
Total Republican residents: $\square$ %
Total Democratic residents: $\square$ %
Answer (2)
Calculate the percentage of Republican residents in County 1: 6520 2470 × 100 = 37.9
Calculate the percentage of Democratic residents in County 1: 6520 4050 × 100 = 62.1
Calculate the percentage of total Republican residents: 24505 14430 × 100 = 58.9
Calculate the percentage of total Democratic residents: 24505 10075 × 100 = 41.1
Explanation
Problem Analysis We will calculate the percentage of Republican residents in County 1, the percentage of Democratic residents in County 1, the percentage of total Republican residents, and the percentage of total Democratic residents. We will round each percentage to the nearest tenth of a percent.
Percentage of Republican Residents in County 1 To find the percentage of Republican residents in County 1, we divide the number of Republican residents in County 1 by the total number of residents in County 1 and multiply by 100: 6520 2470 × 100 The result is 37.9%.
Percentage of Democratic Residents in County 1 To find the percentage of Democratic residents in County 1, we divide the number of Democratic residents in County 1 by the total number of residents in County 1 and multiply by 100: 6520 4050 × 100 The result is 62.1%.
Percentage of Total Republican Residents To find the percentage of total Republican residents, we divide the total number of Republican residents by the overall total number of residents and multiply by 100: 24505 14430 × 100 The result is 58.9%.
Percentage of Total Democratic Residents To find the percentage of total Democratic residents, we divide the total number of Democratic residents by the overall total number of residents and multiply by 100: 24505 10075 × 100 The result is 41.1%.
Final Answer Republican residents of County 1: 37.9% Democratic residents of County 1: 62.1% Total Republican residents: 58.9% Total Democratic residents: 41.1%
Examples
Understanding the distribution of political affiliations within different regions can be useful in political campaigns. For example, a campaign manager can use this data to decide where to focus their resources. If a county is heavily Republican, the campaign might focus on energizing their base rather than trying to persuade Democrats. Similarly, in a county with a high percentage of Democrats, the campaign might focus on voter turnout. The percentages calculated here help in making informed decisions about resource allocation and campaign strategy.
The percentage of Republican residents in County 1 is approximately 37.9%, while the percentage of Democratic residents is approximately 62.1%. Overall, the total percentage of Republican residents across all counties is about 58.9%, and Democratic residents are about 41.1%.
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