Use the table to answer the question.
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
A 40% of the people who preferred the seacoast were 7th graders.
B 32% of 7th-grade campers preferred the mountains.
C 90% of 8th-grade campers preferred the seacoast.
D 70% of the people who preferred mountains were 8th graders.
To find the relative frequency, you need to divide the number of people in a specific category by the total number of people surveyed and then convert it to a percentage.
A. To find the percentage of 7th graders who preferred the seacoast, you divide the number of 7th graders who preferred the seacoast (60) by the total number of people surveyed (300): 60/300 = 0.2. Then, multiply this result by 100 to convert it to a percentage: 0.2 * 100 = 20%. So, the correct answer is not A.
B. To find the percentage of 7th-grade campers who preferred the mountains, you divide the number of 7th-grade campers who preferred the mountains (40) by the total number of 7th-grade campers (100): 40/100 = 0.4. Then, multiply this result by 100 to convert it to a percentage: 0.4 * 100 = 40%. So, the correct answer is B.
C. To find the percentage of 8th-grade campers who preferred the seacoast, you divide the number of 8th-grade campers who preferred the seacoast (90) by the total number of 8th-grade campers (200): 90/200 = 0.45. Then, multiply this result by 100 to convert it to a percentage: 0.45 * 100 = 45%. So, the correct answer is not C.
D. To find the percentage of people who preferred mountains and were 8th graders, you divide the number of 8th graders who preferred mountains (110) by the total number of people who preferred mountains (150): 110/150 ≈ 0.733. Then, multiply this result by 100 to convert it to a percentage: 0.733 * 100 ≈ 73.3%. So, the correct answer is not D.
Therefore, the relative frequency that can be found with the table is B. 32% of 7th-grade campers preferred the mountains.
To find the relative frequency, we need to compare the number of campers in each category with the total number of campers.
A. To find the percentage of people who preferred the seacoast and were in 7th grade, we divide the number of 7th graders who preferred the seacoast (60) by the total number of campers (300) and multiply by 100 to get the percentage: (60/300) * 100 ≈ 20%. Therefore, option A is incorrect.
B. To find the percentage of 7th-grade campers who preferred the mountains, we divide the number of 7th graders who preferred the mountains (40) by the total number of campers (300) and multiply by 100 to get the percentage: (40/300) * 100 ≈ 13.3%. Therefore, option B is incorrect.
C. To find the percentage of 8th-grade campers who preferred the seacoast, we divide the number of 8th graders who preferred the seacoast (90) by the total number of campers (300) and multiply by 100 to get the percentage: (90/300) * 100 = 30%. Therefore, option C is incorrect.
D. To find the percentage of people who preferred the mountains and were in 8th grade, we divide the number of 8th graders who preferred the mountains (110) by the total number of campers (300) and multiply by 100 to get the percentage: (110/300) * 100 ≈ 36.7%. Therefore, option D is correct.
Therefore, the correct answer is D: 70% of the people who preferred mountains were 8th graders.
To determine the relative frequency, we need to find the percentage of a specific group within a category.
A. To find the percentage of people who preferred the seacoast and were in 7th grade:
- We look at the number of 7th graders who preferred the seacoast, which is 60.
- Then, we divide it by the total number of people who preferred the seacoast, which is 100.
- Finally, we multiply the result by 100 to find the percentage.
(60 / 100) * 100 = 60%
Therefore, option A is incorrect as the relative frequency is 60%, not 40%.
B. To find the percentage of 7th-grade campers who preferred the mountains:
- We look at the number of 7th graders who preferred the mountains, which is 40.
- Then, we divide it by the total number of 7th graders, which is 100.
- Finally, we multiply the result by 100 to find the percentage.
(40 / 100) * 100 = 40%
Therefore, option B is incorrect as the relative frequency is 40%, not 32%.
C. To find the percentage of 8th-grade campers who preferred the seacoast:
- We look at the number of 8th graders who preferred the seacoast, which is 90.
- Then, we divide it by the total number of 8th graders, which is 200.
- Finally, we multiply the result by 100 to find the percentage.
(90 / 200) * 100 = 45%
Therefore, option C is incorrect as the relative frequency is 45%, not 90%.
D. To find the percentage of people who preferred mountains and were in 8th grade:
- We look at the number of 8th graders who preferred mountains, which is 110.
- Then, we divide it by the total number of people who preferred mountains, which is 150.
- Finally, we multiply the result by 100 to find the percentage.
(110 / 150) * 100 = 73.3%
Rounded to the nearest tenth, the relative frequency is approximately 73.3%, so option D is the correct answer.