Answer :
To find the relative frequency of students who prefer dogs among the 7th graders, follow these steps:
1. Calculate the total number of 7th grade students:
You need to sum up all the categories of students in the 7th grade:
- Prefers Cats: 36
- Prefers Dogs: 8
- No Preference: 2
[tex]\[ \text{Total students in 7th grade} = 36 + 8 + 2 = 46 \][/tex]
2. Determine the number of 7th graders who prefer dogs:
According to the table, 8 students prefer dogs.
3. Calculate the relative frequency:
To find the relative frequency, divide the number of students who prefer dogs by the total number of students and then multiply by 100 to convert it to a percentage:
[tex]\[ \text{Relative frequency} = \left( \frac{\text{Number of students who prefer dogs}}{\text{Total number of students}} \right) \times 100 \][/tex]
Plugging in the numbers:
[tex]\[ \text{Relative frequency} = \left( \frac{8}{46} \right) \times 100 \approx 17.391304347826086 \% \][/tex]
4. Round the percentage to the nearest tenth:
When you round 17.391304347826086 to the nearest tenth, you get:
[tex]\[ \text{Rounded relative frequency} = 17.4\% \][/tex]
Therefore, the relative frequency of 7th graders who prefer dogs is 17.4%, which corresponds to the last option.
So, the correct answer is:
[tex]\[ \boxed{17.4\%} \][/tex]
1. Calculate the total number of 7th grade students:
You need to sum up all the categories of students in the 7th grade:
- Prefers Cats: 36
- Prefers Dogs: 8
- No Preference: 2
[tex]\[ \text{Total students in 7th grade} = 36 + 8 + 2 = 46 \][/tex]
2. Determine the number of 7th graders who prefer dogs:
According to the table, 8 students prefer dogs.
3. Calculate the relative frequency:
To find the relative frequency, divide the number of students who prefer dogs by the total number of students and then multiply by 100 to convert it to a percentage:
[tex]\[ \text{Relative frequency} = \left( \frac{\text{Number of students who prefer dogs}}{\text{Total number of students}} \right) \times 100 \][/tex]
Plugging in the numbers:
[tex]\[ \text{Relative frequency} = \left( \frac{8}{46} \right) \times 100 \approx 17.391304347826086 \% \][/tex]
4. Round the percentage to the nearest tenth:
When you round 17.391304347826086 to the nearest tenth, you get:
[tex]\[ \text{Rounded relative frequency} = 17.4\% \][/tex]
Therefore, the relative frequency of 7th graders who prefer dogs is 17.4%, which corresponds to the last option.
So, the correct answer is:
[tex]\[ \boxed{17.4\%} \][/tex]
