To calculate the relative frequency of 7th graders who prefer dogs, we first need to find the total number of 7th graders.
From the table:
- Students who prefer cats: 36
- Students who prefer dogs: 8
- Students with no preference: 2
Now, we can find the total number of 7th graders:
\[ \text{Total 7th graders} = (\text{prefers cats}) + (\text{prefers dogs}) + (\text{no preference}) \] \[ \text{Total 7th graders} = 36 + 8 + 2 = 46 \]
Next, we determine the relative frequency of 7th graders who prefer dogs:
\[ \text{Relative frequency of 7th graders who prefer dogs} = \frac{\text{Number of 7th graders who prefer dogs}}{\text{Total number of 7th graders}} \] \[ = \frac{8}{46} \]
Now, we calculate that fraction:
\[ \frac{8}{46} \approx 0.1739 \]
To convert this to a percentage, we multiply by 100:
\[ 0.1739 \times 100 \approx 17.39% \]
Rounding this to the nearest tenth, we get:
\[ \approx 17.4% \]
Thus, the relative frequency of students who prefer dogs and are 7th graders is 17.4%.