Question

determining relative frequencies as percentages
residents of three counties were polled to find the percentage of residents who are republican or democrat.
find the following relative frequencies to the nearest tenth of a percent.
republican residents of county 1: 37.9 %
democratic residents of county 1: 62.1 %
total republican residents: 58.6 %
total democratic residents: 41.1 %

	democrat	republican	total
county 2	3,925	6,010	9,935
county 3	2,100	5,950	8,050
total	10,075	14,430	24,505

Explanation:

Republican residents of County 1

Step1: Identify values

Republican in County 1: \( 2470 \), Total in County 1: \( 6520 \)

Step2: Calculate relative frequency

Relative frequency \( = \frac{2470}{6520} \times 100 \)
\( \frac{2470}{6520} \approx 0.3788 \), \( 0.3788 \times 100 \approx 37.9\% \)

Democratic residents of County 1

Step1: Identify values

Democratic in County 1: \( 4050 \), Total in County 1: \( 6520 \)

Step2: Calculate relative frequency

Relative frequency \( = \frac{4050}{6520} \times 100 \)
\( \frac{4050}{6520} \approx 0.6212 \), \( 0.6212 \times 100 \approx 62.1\% \)

Total Republican residents

Step1: Identify values

Total Republican: \( 14430 \), Total overall: \( 24505 \)

Step2: Calculate relative frequency

Relative frequency \( = \frac{14430}{24505} \times 100 \)
\( \frac{14430}{24505} \approx 0.5888 \), \( 0.5888 \times 100 \approx 58.9\% \) (Note: There was a typo in the original, correct is ~58.9)

Total Democratic residents

Answer:

s:
Republican residents of County 1: \( 37.9\% \)
Democratic residents of County 1: \( 62.1\% \)
Total Republican residents: \( 58.9\% \) (corrected from 58.0)
Total Democratic residents: \( 41.1\% \)