this table displayers 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 preferce | 2 | 6 |

what is the relative frequency of students who prefer dohs who are 7th graders? round the percentage to the nearest tenth

76.5%
23.5%
17.4%
8%

1 answer

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%.