Use the table to answer the 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 largest joint relative frequency is fourth graders with a pet.
The largest joint relative frequency is fourth graders with a pet.

The smallest joint relative frequency is third graders without a pet.

1 answer

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:

  1. 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."
  2. 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.
  3. 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.
  4. 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.