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Students Seacoast Mountains Totals 7th Grade 60 40 100 8th Grade 90 110 200 Totals 150 150 300 Gloria surveyed all of the campers to determine their preferred field trip. The results are displayed in the table. Which of the following is a relative frequency that can be found with the table? Round the percentage to the nearest tenth. (1 point) Responses 40% of the people who preferred the seacoast were 7th graders. 40% of the people who preferred the seacoast were 7th graders. 70% of the people who preferred mountains were 8th graders. 70% of the people who preferred mountains were 8th graders. 90% of 8th-grade campers preferred the seacoast. 90% of 8th-grade campers preferred the seacoast. 32% of 7th-grade campers preferred the mountains.

1 answer

To calculate the relative frequencies based on the given table, we can derive percentages from the data:

  1. Total number of students: 300 (150 7th graders + 150 8th graders)

  2. Seacoast preferences:

    • 7th Graders: 60

    • 8th Graders: 90

    • Total Seacoast: 150

    • Relative frequency of 7th graders who preferred the seacoast: \[ \text{Relative frequency} = \frac{60}{150} \times 100 = 40% \]

  3. Mountain preferences:

    • 7th Graders: 40

    • 8th Graders: 110

    • Total Mountains: 150

    • Relative frequency of 8th graders who preferred the mountains: \[ \text{Relative frequency} = \frac{110}{150} \times 100 = \frac{110}{150} \times 100 \approx 73.3% \]

    • Relative frequency of 8th graders who preferred the seacoast: \[ \text{Relative frequency} = \frac{90}{150} \times 100 = 60% \]

  4. Relative frequency of 7th graders who preferred the mountains: \[ \text{Relative frequency} = \frac{40}{150} \times 100 \approx 26.7% \]

Now, to answer the question, we'll consider the given options:

  • 40% of the people who preferred the seacoast were 7th graders. (This is correct.)
  • 70% of the people who preferred mountains were 8th graders. (This is approximately 73.3%, so it's not correct.)
  • 90% of 8th-grade campers preferred the seacoast. (This is 60%, so it's not correct.)
  • 32% of 7th-grade campers preferred the mountains. (This is approximately 26.7%, so it's not correct.)

Thus, the correct relative frequency can be stated as: 40% of the people who preferred the seacoast were 7th graders.