Ask a New Question
Menu

Students Seacoast Mountains Totals

7th Grade 60

40
100
8th Grade 90

110
200
Totals
150
150
300
Calculating the survey's relative frequency.
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)
• 90% of 8th-grade campers preferred the seacoast.
• 70% of the people who preferred mountains were 8th graders.
• 32% of 7th-grade campers preferred the mountains.
40% of the people who preferred the seacoast were 7th graders.

1 answer

To calculate the relative frequencies from the data you provided in the table, we'll first clarify the details.

From your data:

  • 7th Grade (Seacoast): 60

  • 7th Grade (Mountains): 40

  • Total 7th Grade: 100

  • 8th Grade (Seacoast): 90

  • 8th Grade (Mountains): 110

  • Total 8th Grade: 200

  • Overall totals:

    • Seacoast: 150 (60+90)
    • Mountains: 150 (40+110)
    • Grand Total: 300 (100 + 200)

Now, let's analyze each of the statements given:

  1. 90% of 8th-grade campers preferred the seacoast.
    To check this, we calculate the relative frequency of 8th graders who preferred the seacoast: \(\frac{90}{200} \times 100 = 45%\)
    This statement is false.

  2. 70% of the people who preferred mountains were 8th graders.
    Calculate the number of 8th graders who preferred mountains and the total number of people who preferred mountains:
    \(\frac{110}{150} \times 100 = 73.3%\)
    This statement is true.

  3. 32% of 7th-grade campers preferred the mountains.
    Calculate the relative frequency of 7th graders who preferred mountains:
    \(\frac{40}{100} \times 100 = 40%\)
    This statement is false.

  4. 40% of the people who preferred the seacoast were 7th graders.
    Calculate the relative frequency of 7th graders who preferred the seacoast:
    \(\frac{60}{150} \times 100 = 40%\)
    This statement is true.

So the valid statements we found with their corresponding relative frequencies are:

  • 70% of the people who preferred mountains were 8th graders (73.3% rounded).
  • 40% of the people who preferred the seacoast were 7th graders.

Thus, both the second and fourth statements can be considered correct based on the calculations.