Students

7th Grade
8th Grade
Totals


Seacoast
70
90
160


Mountains
40
110
150


Totals
110
200
310




​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. 90% of 8th-grade campers preferred the seacoast. 90% of 8th-grade campers preferred the seacoast. 70% of the people who preferred mountains were 8th graders. 70% of the people who preferred mountains were 8th graders. 32% of 7th-grade campers preferred the mountains.

1 answer

To determine the correct relative frequencies based on the table provided, we can follow these steps:

1. Analyze the data:

  • Seacoast 7th graders: 70
  • Seacoast 8th graders: 90
  • Mountains 7th graders: 40
  • Mountains 8th graders: 110

2. Total number breakdown:

  • Total Seacoast campers: 160 (70 + 90)
  • Total Mountains campers: 150 (40 + 110)
  • Overall total campers: 310

3. Calculate the relative frequencies:

  • For 7th graders who preferred the Seacoast: \[ \text{Relative frequency} = \left(\frac{70}{160}\right) \times 100 = 43.75% \approx 43.8% \]
  • For 8th graders who preferred the Seacoast: \[ \text{Relative frequency} = \left(\frac{90}{200}\right) \times 100 = 45% \]
  • For 8th graders who preferred the Mountains: \[ \text{Relative frequency} = \left(\frac{110}{150}\right) \times 100 = 73.33% \approx 73.3% \]
  • For 7th graders who preferred the Mountains: \[ \text{Relative frequency} = \left(\frac{40}{150}\right) \times 100 = 26.67% \approx 26.7% \]

4. Evaluate the response options:

  • "40% of the people who preferred the seacoast were 7th graders." - Incorrect (actual is 43.8%).
  • "90% of 8th-grade campers preferred the seacoast." - Incorrect (actual is 45%).
  • "70% of the people who preferred mountains were 8th graders." - Incorrect.
  • "32% of 7th-grade campers preferred the mountains." - Incorrect (actual is 26.7%).

None of the given responses seem correct based on the calculations and the data provided so, based on the calculations, none of the relative frequencies accurately reflect the information in the table.

However, the closest statement would be the first one regarding the 7th graders who preferred the Seacoast, which is approximately 43.8%, indicating that it would not be satisfactory in this context. Therefore, none of the choices provided are accurate.