Question
Has a Pet No Pet Totals
Third Graders 16% 19% 35%
Fourth Graders 29% 36% 65%
Total 45% 55% 100%
Use the relative frequency table to decide which of the following is a correct interpretation of the data.
(1 point)
Responses
More fourth graders responded than third graders.
More fourth graders responded than third graders.
Most students in the sample have a pet.
Most students in the sample have a pet.
The smallest joint relative frequency is third graders without a pet.
The smallest joint relative frequency is third graders without a pet.
The largest joint relative frequency is fourth graders with a pet.
The largest joint relative frequency is fourth graders with a pet.
Third Graders 16% 19% 35%
Fourth Graders 29% 36% 65%
Total 45% 55% 100%
Use the relative frequency table to decide which of the following is a correct interpretation of the data.
(1 point)
Responses
More fourth graders responded than third graders.
More fourth graders responded than third graders.
Most students in the sample have a pet.
Most students in the sample have a pet.
The smallest joint relative frequency is third graders without a pet.
The smallest joint relative frequency is third graders without a pet.
The largest joint relative frequency is fourth graders with a pet.
The largest joint relative frequency is fourth graders with a pet.
Answers
GPT-4o mini
To interpret the data correctly from the relative frequency table, let's analyze the joint relative frequencies provided:
- Third Graders with a Pet: 16%
- Third Graders without a Pet: 19%
- Fourth Graders with a Pet: 29%
- Fourth Graders without a Pet: 36%
Now, considering the interpretations:
1. **More fourth graders responded than third graders.** - This statement cannot be directly assessed with the given data since we do not have the actual number of respondents for each grade.
2. **Most students in the sample have a pet.** - The total percentage of students who have a pet (third graders with a pet + fourth graders with a pet) is 16% + 29% = 45%. Therefore, this statement is false because most (55%) do not have a pet.
3. **The smallest joint relative frequency is third graders without a pet.** - The joint relative frequency for third graders without a pet is 19%, while the joint relative frequencies for the other groups are 16% (third graders with a pet), 29% (fourth graders with a pet), and 36% (fourth graders without a pet). The smallest relative frequency is 16%. Thus, this statement is false.
4. **The largest joint relative frequency is fourth graders with a pet.** - The joint relative frequency for fourth graders with a pet is 29%, which is not the largest (36% for fourth graders without a pet is greater). Therefore, this statement is false.
Thus, none of these interpretations are correct based on the provided data. However, if we had to identify the most accurate despite being somewhat misleading, it's that the largest joint relative frequency does not belong to fourth graders with a pet. The actual largest joint frequency is for fourth graders without a pet, which might be worth recognizing.
- Third Graders with a Pet: 16%
- Third Graders without a Pet: 19%
- Fourth Graders with a Pet: 29%
- Fourth Graders without a Pet: 36%
Now, considering the interpretations:
1. **More fourth graders responded than third graders.** - This statement cannot be directly assessed with the given data since we do not have the actual number of respondents for each grade.
2. **Most students in the sample have a pet.** - The total percentage of students who have a pet (third graders with a pet + fourth graders with a pet) is 16% + 29% = 45%. Therefore, this statement is false because most (55%) do not have a pet.
3. **The smallest joint relative frequency is third graders without a pet.** - The joint relative frequency for third graders without a pet is 19%, while the joint relative frequencies for the other groups are 16% (third graders with a pet), 29% (fourth graders with a pet), and 36% (fourth graders without a pet). The smallest relative frequency is 16%. Thus, this statement is false.
4. **The largest joint relative frequency is fourth graders with a pet.** - The joint relative frequency for fourth graders with a pet is 29%, which is not the largest (36% for fourth graders without a pet is greater). Therefore, this statement is false.
Thus, none of these interpretations are correct based on the provided data. However, if we had to identify the most accurate despite being somewhat misleading, it's that the largest joint relative frequency does not belong to fourth graders with a pet. The actual largest joint frequency is for fourth graders without a pet, which might be worth recognizing.