To analyze the relative frequency table for the provided data, let's first clarify the joint relative frequencies:
- 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 we can evaluate the given responses:
-
More fourth graders responded than third graders.
- This is not correct; the table shows that 35% of the sample are third graders, while 65% are fourth graders. However, this statement could be interpreted ambiguously without context about "responded."
-
Most students in the sample have a pet.
- This statement is true. Looking at the totals, 45% have a pet, which is less than 50%. Therefore, this statement is incorrect.
-
The largest joint relative frequency is fourth graders with a pet.
- This is incorrect. The largest joint relative frequency is actually fourth graders without a pet (36%), which is greater than the joint relative frequencies of either third graders or fourth graders with pets.
-
The smallest joint relative frequency is third graders without a pet.
- This is true since the frequency for third graders without a pet is 19%, which is indeed the smallest amount relative to the other values.
Thus, the correct interpretation of the data from the options provided is:
The smallest joint relative frequency is third graders without a pet.