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Use the table to answer the question. Calculating the survey's relative frequency. 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 32% of 7th-grade campers preferred the mountains. 32% of 7th-grade campers preferred the mountains. 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. 40% of the people who preferred the seacoast were 7th graders.

1 answer

To find the relative frequencies, we need to calculate the percentages based on the totals provided in the table.

  1. Calculate the percentage of 7th-grade campers who preferred the mountains:

    • Number of 7th-grade campers who preferred the mountains = 40
    • Total number of 7th-grade campers = 100
    • Relative frequency = (40 / 100) * 100 = 40%

  2. Calculate the percentage of people who preferred mountains who were 8th graders:

    • Total number of people who preferred the mountains = 40 (7th graders) + 110 (8th graders) = 150
    • Number of 8th graders who preferred the mountains = 110
    • Relative frequency = (110 / 150) * 100 = 73.3%

  3. Calculate the percentage of 8th-grade campers who preferred the seacoast:

    • Number of 8th-grade campers who preferred the seacoast = 90
    • Total number of 8th-grade campers = 200
    • Relative frequency = (90 / 200) * 100 = 45%

  4. Calculate the percentage of people who preferred the seacoast who were 7th graders:

    • Total number of people who preferred the seacoast = 60 (7th graders) + 90 (8th graders) = 150
    • Number of 7th graders who preferred the seacoast = 60
    • Relative frequency = (60 / 150) * 100 = 40%

From these calculations, we can evaluate the provided responses:

  • "32% of 7th-grade campers preferred the mountains." (False, it's 40%)
  • "70% of the people who preferred mountains were 8th graders." (True, it's approximately 73.3%)
  • "90% of 8th-grade campers preferred the seacoast." (False, it's 45%)
  • "40% of the people who preferred the seacoast were 7th graders." (True, it's exactly 40%)

So, two correct relative frequencies can be found in the table:

  • 70% of the people who preferred mountains were 8th graders.
  • 40% of the people who preferred the seacoast were 7th graders.

The relative frequencies that match the responses are the second option and the last option. However, only one can be considered correct based on the original question's format. So, the most directly applicable relative frequency from the options is:

70% of the people who preferred mountains were 8th graders.