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: %
Democratic residents of County 1: %
Total Republican residents: %
Total Democratic residents: %
Answer (1)
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% .
37.9% , 62.1% , 58.9% , 41.1%
Explanation
Understand the problem and provided data We are given a table with the number of Democrat and Republican residents in three counties. We need to find the relative frequencies (percentages) for specific categories.
Calculate Republican residents in County 1 First, we need to calculate 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.
Calculate the percentage The number of Republican residents in County 1 is 2,470, and the total number of residents in County 1 is 6,520. Therefore, the percentage is: 6520 2470 × 100 ≈ 37.9%
Calculate 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 multiply by 100.
Calculate the percentage The number of Democratic residents in County 1 is 4,050, and the total number of residents in County 1 is 6,520. Therefore, the percentage is: 6520 4050 × 100 ≈ 62.1%
Calculate total Republican residents Now, we calculate the percentage of total Republican residents. We divide the total number of Republican residents by the total number of residents and multiply by 100.
Calculate the percentage The total number of Republican residents is 14,430, and the total number of residents is 24,505. Therefore, the percentage is: 24505 14430 × 100 ≈ 58.9%
Calculate total Democratic residents Finally, we calculate the percentage of total Democratic residents. We divide the total number of Democratic residents by the total number of residents and multiply by 100.
Calculate the percentage The total number of Democratic residents is 10,075, and the total number of residents is 24,505. Therefore, the percentage is: 24505 10075 × 100 ≈ 41.1%
State the final answer Therefore, the relative frequencies are: 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 a population can be useful in various real-world scenarios. For example, political campaigns use this information to tailor their messaging to specific demographics. Similarly, governments can use this data to ensure fair representation and resource allocation across different regions. Market research can also benefit from understanding political leanings, as it can influence consumer behavior and preferences. By analyzing these percentages, one can gain insights into the political landscape and make informed decisions.
