Use the table to answer the question.

Preference 7th Graders 8th Graders
Prefers Cats 36 22
Prefers Dogs 8 26
No Preference 2 6
What is the relative frequency of 8th graders who prefer cats? Round the percentage to the nearest tenth.

(1 point)
Responses

22%
22%

40.7%
40.7%

78.2%
78.2%

37.9%

1 answer

To find the relative frequency of 8th graders who prefer cats, we need to use the formula for relative frequency:

\[ \text{Relative Frequency} = \frac{\text{Number of 8th Graders who prefer Cats}}{\text{Total number of 8th Graders}} \]

From the table provided:

  • The number of 8th graders who prefer cats is 22.
  • The total number of 8th graders is the sum of those who prefer cats, prefer dogs, and have no preference:

\[ \text{Total number of 8th Graders} = 22 + 26 + 6 = 54 \]

Now, we can calculate the relative frequency:

\[ \text{Relative Frequency} = \frac{22}{54} \]

Calculating that gives us:

\[ \text{Relative Frequency} \approx 0.4074 \]

To express this as a percentage:

\[ 0.4074 \times 100 \approx 40.74% \]

Rounding to the nearest tenth, we get:

\[ 40.7% \]

Thus, the relative frequency of 8th graders who prefer cats is 40.7%.