To find the relative frequency of students who prefer cats among the 8th graders, we need to follow these steps:
- Count the total number of 8th graders and the number who prefer cats.
- Calculate the relative frequency using the formula:
\[ \text{Relative Frequency} = \frac{\text{Number of 8th graders who prefer cats}}{\text{Total number of 8th graders}} \times 100 \]
Step 1: Gather the data
From the data given:
- 8th graders who prefer cats: 22
- 8th graders who prefer dogs: 26
- 8th graders with no preference: 6
Step 2: Calculate the total number of 8th graders
\[ \text{Total 8th graders} = 22 + 26 + 6 = 54 \]
Step 3: Calculate the relative frequency
Now, we calculate the relative frequency of 8th graders who prefer cats:
\[ \text{Relative Frequency} = \frac{22}{54} \times 100 \]
Calculating that:
\[ \frac{22}{54} \approx 0.407407 \]
Now, we convert this to a percentage:
\[ 0.407407 \times 100 \approx 40.7407 \]
Step 4: Round to the nearest tenth
Rounding 40.7407 to the nearest tenth gives us 40.7%.
It appears that this percentage does not match any of the answer choices provided. Please verify the problem statement for additional context or numerical accuracy, but based on the data provided, the relative frequency should be 40.7%.