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.
(1 point)
8%
23.5%
76.5%
17.4%

1 answer

To calculate the relative frequency of 7th graders who prefer dogs, we need to determine the number of 7th graders who prefer dogs compared to the total number of 7th graders surveyed.

From the table:

  • Number of 7th graders who prefer dogs: 8
  • Number of 7th graders who prefer cats: 36
  • Number of 7th graders with no preference: 2

First, we calculate the total number of 7th graders surveyed: \[ \text{Total 7th graders} = (\text{Prefers Cats}) + (\text{Prefers Dogs}) + (\text{No Preference}) = 36 + 8 + 2 = 46 \]

Next, we calculate the relative frequency of 7th graders who prefer dogs: \[ \text{Relative frequency} = \frac{\text{Number of 7th graders who prefer dogs}}{\text{Total number of 7th graders}} = \frac{8}{46} \]

Now we can calculate this fraction: \[ \frac{8}{46} \approx 0.1739 \]

To express this as a percentage, we multiply by 100: \[ 0.1739 \times 100 \approx 17.39% \]

Rounding to the nearest tenth, we get: \[ 17.4% \]

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