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: [$\square$] 37.9 %
Democratic residents of County 1: [$\square$] 62.1 %
Total Republican residents: [$\square$] 58.9 %
Total Democratic residents: [$\square$] 41.1 %
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 . The given percentages are correct: 37.9% , 62.1% , 58.9% , 41.1%
Explanation
Analyze the problem and data We are given a two-way table showing the distribution of Democrats and Republicans across three counties. The goal is to verify the provided percentages for specific categories.
Calculate percentage of Republican residents in County 1 First, we calculate the percentage of Republican residents in County 1. This is done by dividing the number of Republican residents in County 1 by the total number of residents in County 1, and then multiplying by 100. That is, we calculate 6520 2470 × 100 . The result of this calculation is approximately 37.88%.
Calculate percentage of Democratic residents in County 1 Next, we calculate 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 then multiply by 100. That is, we calculate 6520 4050 × 100 . The result of this calculation is approximately 62.12%.
Calculate percentage of total Republican residents Now, we calculate the percentage of total Republican residents. We divide the total number of Republican residents by the overall total number of residents, and then multiply by 100. That is, we calculate 24505 14430 × 100 . The result of this calculation is approximately 58.89%.
Calculate percentage of total Democratic residents Finally, we calculate the percentage of total Democratic residents. We divide the total number of Democratic residents by the overall total number of residents, and then multiply by 100. That is, we calculate 24505 10075 × 100 . The result of this calculation is approximately 41.11%.
Conclusion Comparing our calculated percentages to the given percentages, we see that they match to the nearest tenth of a percent. Therefore, the given percentages are correct.
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 relative frequencies is crucial in many real-world scenarios. For instance, political analysts use these calculations to understand voter demographics and predict election outcomes. Similarly, marketers use relative frequencies to analyze customer segments and tailor their campaigns. In public health, these calculations help track the prevalence of diseases within different populations, guiding resource allocation and intervention strategies. These percentages provide a clear snapshot of the composition of different groups, enabling informed decision-making across various fields.
The calculations show that 37.9% of County 1's residents are Republican and 62.1% are Democratic. Overall, 58.9% of surveyed residents are Republican while 41.1% are Democratic. These results verify the percentages provided in the question.
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