Question

This table displays the number of 7th and 8th grade students who prefer either dogs or cats.
Preference 7th Graders 8th Graders
Prefers Cats 36 22
Prefers Dogs 8 26
No Preference 2 6
What is the relative frequency of students who prefer dogs who are 7th graders? Round the percentage to the nearest tenth.

Answer 1

To find the relative frequency of 7th graders who prefer dogs, we first need to determine the total number of 7th graders.

From the table, the number of 7th graders is calculated as follows:

- Prefers Cats: 36
- Prefers Dogs: 8
- No Preference: 2

Total number of 7th graders = 36 + 8 + 2 = 46

Next, we find the relative frequency of 7th graders who prefer dogs. This is calculated by dividing the number of 7th graders who prefer dogs by the total number of 7th graders:

\[
\text{Relative Frequency} = \frac{\text{Number of 7th Graders who prefer Dogs}}{\text{Total Number of 7th Graders}} = \frac{8}{46}
\]

Now, we calculate the relative frequency:

\[
\frac{8}{46} \approx 0.1739
\]

To express this as a percentage, we multiply by 100:

\[
0.1739 \times 100 \approx 17.39\%
\]

Rounding to the nearest tenth of a percent gives us:

\[
\text{Relative Frequency} \approx 17.4\%
\]

Therefore, the relative frequency of students who prefer dogs and are 7th graders is **17.4%**.