A survey was conducted with high school students in each grade to see how many participate in sports. The data are shown below.
| | 9 | 10 | 11 | 12 | Total |
| :----- | :- | :- | :- | :- | :---- |
| Sports | 63 | 52 | 35 | 41 | |
| No Sports | 51 | 45 | 21 | 36 | |
| Total | | | | | 344 |
Which statement is true about the marginal frequencies in this table?
A. 191 students play sports and 150 students do not.
B. 153 students do not participate in sports and seventy-ilve 12th graders were surveyed
C. 153 students do not participate in sports and 190 do.
D. 191 students play sports and ninety-seven 10th graders were surveyed.
Answer (1)
Calculate the total number of students who play sports: 63 + 52 + 35 + 41 = 191 .
Calculate the total number of students who do not play sports: 51 + 45 + 21 + 36 = 153 .
Calculate the total number of 10th graders: 52 + 45 = 97 .
The true statement is: 191 students play sports and ninety-seven 10th graders were surveyed. 191 students play sports and ninety-seven 10th graders were surveyed.
Explanation
Understand the problem and provided data We are given a table showing the number of high school students in each grade who participate in sports and who do not. The question asks us to identify the true statement about the marginal frequencies in this table. Marginal frequencies refer to the row and column totals in the table.
Calculate the total number of students who participate in sports First, let's calculate the total number of students who participate in sports. We sum the numbers in the 'Sports' row: 63 + 52 + 35 + 41 = 191 . So, 191 students play sports.
Calculate the total number of students who do not participate in sports Next, let's calculate the total number of students who do not participate in sports. We sum the numbers in the 'No Sports' row: 51 + 45 + 21 + 36 = 153 . So, 153 students do not play sports.
Calculate the total number of 10th graders Now, let's calculate the total number of 10th graders surveyed: 52 + 45 = 97 . So, 97 students are in 10th grade.
Calculate the total number of 12th graders Finally, let's calculate the total number of 12th graders surveyed: 41 + 36 = 77 . So, 77 students are in 12th grade.
Compare the calculated marginal frequencies with the statements provided Now we compare our calculations to the given statements:
"191 students play sports and 150 students do not." - Incorrect, since 153 students do not play sports.
"153 students do not participate in sports and seventy-ilve 12th graders were surveyed" - Incorrect, since 77 students are in 12th grade, not 75.
"153 students do not participate in sports and 190 do." - Incorrect, since 191 students play sports, not 190.
"191 students play sports and ninety-seven 10th graders were surveyed." - Correct.
Examples
Marginal frequencies are useful in understanding the distribution of data in surveys and statistical analyses. For example, if a school wants to know how many students participate in extracurricular activities, they can use marginal frequencies to quickly see the total number of students involved in each activity and the total number of students overall. This helps in resource allocation and planning.
