To determine the relative frequency of 7th graders who prefer dogs, we first need to find the total number of 7th graders and the number of 7th graders who prefer dogs.
From the table:
- 7th graders who prefer dogs: 8
- 7th graders who prefer cats: 36
- 7th graders with no preference: 2
First, we calculate the total number of 7th graders:
\[ \text{Total 7th Graders} = \text{Prefers Cats} + \text{Prefers Dogs} + \text{No Preference} = 36 + 8 + 2 = 46 \]
Now, we can calculate the relative frequency of 7th graders who prefer dogs:
\[ \text{Relative Frequency} = \frac{\text{Number of 7th Graders who prefer Dogs}}{\text{Total Number of 7th Graders}} = \frac{8}{46} \]
Next, we convert this fraction into a percentage:
\[ \text{Relative Frequency as a Percentage} = \left( \frac{8}{46} \right) \times 100 \approx 17.3913% \]
Finally, rounding to the nearest tenth of a percent gives us:
\[ \text{Relative Frequency} \approx 17.4% \]
Thus, the relative frequency of students who prefer dogs who are 7th graders is 17.4%.