To find the relative frequency of 7th graders who prefer dogs, we first need to determine the total number of 7th graders in the survey.
From the table:
- 7th graders who prefer cats: 36
- 7th graders who prefer dogs: 8
- 7th graders with no preference: 2
Now, we calculate the total number of 7th graders:
\[ \text{Total 7th Graders} = 36 + 8 + 2 = 46 \]
Next, we find the relative frequency of 7th graders who prefer dogs:
\[ \text{Relative Frequency} = \frac{\text{Number of 7th Graders Preferring Dogs}}{\text{Total Number of 7th Graders}} = \frac{8}{46} \]
Now, we calculate \( \frac{8}{46} \):
\[ \frac{8}{46} \approx 0.1739 \]
To express this as a percentage, we multiply by 100:
\[ 0.1739 \times 100 \approx 17.39% \]
When rounding to the nearest tenth of a percent, this is approximately:
\[ 17.4% \]
Thus, the final answer is:
17.4%