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
Analyze the problem and data We are given a table with the number of Democrat and Republican residents in three counties. We need to verify the given percentages for:
Republican residents of County 1
Democratic residents of County 1
Total Republican residents
Total Democratic residents
Calculate percentage of Republican residents in County 1 First, let's calculate the percentage of Republican residents in County 1. We have 2,470 Republican residents out of a total of 6,520 residents in County 1. The percentage is calculated as: Total residents in County 1 Republican residents in County 1 × 100 = 6520 2470 × 100 The result of this calculation is approximately 37.88%. Rounding to the nearest tenth of a percent, we get 37.9%.
Calculate percentage of Democratic residents in County 1 Next, let's calculate the percentage of Democratic residents in County 1. We have 4,050 Democratic residents out of a total of 6,520 residents in County 1. The percentage is calculated as: Total residents in County 1 Democratic residents in County 1 × 100 = 6520 4050 × 100 The result of this calculation is approximately 62.12%. Rounding to the nearest tenth of a percent, we get 62.1%.
Calculate percentage of total Republican residents Now, let's calculate the percentage of total Republican residents. We have 14,430 Republican residents out of a total of 24,505 residents. The percentage is calculated as: Total residents Total Republican residents × 100 = 24505 14430 × 100 The result of this calculation is approximately 58.89%. Rounding to the nearest tenth of a percent, we get 58.9%.
Calculate percentage of total Democratic residents Finally, let's calculate the percentage of total Democratic residents. We have 10,075 Democratic residents out of a total of 24,505 residents. The percentage is calculated as: Total residents Total Democratic residents × 100 = 24505 10075 × 100 The result of this calculation is approximately 41.11%. Rounding to the nearest tenth of a percent, we get 41.1%.
Conclusion Therefore, the calculated percentages match the given percentages.
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 assess voter demographics and predict election outcomes. Similarly, marketers use relative frequencies to understand customer preferences and tailor their campaigns. In public health, these calculations help track the prevalence of diseases within different populations, guiding resource allocation and intervention strategies. By calculating the proportion of different groups within a population, we gain valuable insights for decision-making in various fields.
The percentages of residents in County 1 are 37.9% Republican and 62.1% Democratic. Overall, 58.9% of residents across all counties are Republican, while 41.1% are Democrats.
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