Question
After a night at an arcade, a sixth-grade class compiled data on the number of tickets each student won. The class finds that the mean number of tickets was 30. Which of the following statements must be true? Select three that apply.
Each student won 30 tickets.
The average number of tickets is 30 per student.
The total number of tickets won by the class was 30.
Half of the class won more than 30 tickets, while the other half won less than 30 tickets.
If the total number of tickets won by the class is divided by the number of students, the result is 30 tickets.
If all of the tickets won by the class are redistributed equally among the class, each student would receive 30 tickets.
Each student won 30 tickets.
The average number of tickets is 30 per student.
The total number of tickets won by the class was 30.
Half of the class won more than 30 tickets, while the other half won less than 30 tickets.
If the total number of tickets won by the class is divided by the number of students, the result is 30 tickets.
If all of the tickets won by the class are redistributed equally among the class, each student would receive 30 tickets.
Answers
GPT-4o mini
Based on the information provided that the mean number of tickets won by the students in the class was 30, the following statements must be true:
1. **The average number of tickets is 30 per student.**
(This statement is true, as "mean" and "average" are synonymous terms in this context.)
2. **If the total number of tickets won by the class is divided by the number of students, the result is 30 tickets.**
(This statement is directly related to the definition of the mean; it's calculated by dividing the total number of tickets by the number of students.)
3. **If all of the tickets won by the class are redistributed equally among the class, each student would receive 30 tickets.**
(This follows logically as well; redistributing the total tickets equally will yield the mean value.)
The other statements are not necessarily true:
- **Each student won 30 tickets.** (This is not true; some students may have won more and others less.)
- **The total number of tickets won by the class was 30.** (The total could be any number as long as the average is 30, depending on how many students there are and how many tickets each won.)
- **Half of the class won more than 30 tickets, while the other half won less than 30 tickets.** (This is not true; the distribution of tickets can vary widely without enforcing that half must be above and half below the mean.)
Thus, the correct statements are 2, 5, and 6.
1. **The average number of tickets is 30 per student.**
(This statement is true, as "mean" and "average" are synonymous terms in this context.)
2. **If the total number of tickets won by the class is divided by the number of students, the result is 30 tickets.**
(This statement is directly related to the definition of the mean; it's calculated by dividing the total number of tickets by the number of students.)
3. **If all of the tickets won by the class are redistributed equally among the class, each student would receive 30 tickets.**
(This follows logically as well; redistributing the total tickets equally will yield the mean value.)
The other statements are not necessarily true:
- **Each student won 30 tickets.** (This is not true; some students may have won more and others less.)
- **The total number of tickets won by the class was 30.** (The total could be any number as long as the average is 30, depending on how many students there are and how many tickets each won.)
- **Half of the class won more than 30 tickets, while the other half won less than 30 tickets.** (This is not true; the distribution of tickets can vary widely without enforcing that half must be above and half below the mean.)
Thus, the correct statements are 2, 5, and 6.