To find the relative frequencies, we will calculate the proportions of preferences for each music genre among the 10th and 11th graders based on the provided data.
Data Summary:
-
10th Grade:
- Hip-Hop: 112
- Pop: 53
- Total: 165
-
11th Grade:
- Hip-Hop: 98
- Pop: 147
- Total: 245
-
Overall Total:
- Hip-Hop: 210
- Pop: 200
- Grand Total: 410
Relative Frequencies for 10th Graders:
To find the proportion of 10th graders who prefer each genre:
-
Preference for Hip-Hop:
\( \frac{112}{165} \approx 0.678 \) (or 67.8%) -
Preference for Pop:
\( \frac{53}{165} \approx 0.321 \) (or 32.1%)
Relative Frequencies for 11th Graders:
To find the proportion of 11th graders who prefer each genre:
-
Preference for Hip-Hop:
\( \frac{98}{245} \approx 0.4 \) (or 40%) -
Preference for Pop:
\( \frac{147}{245} \approx 0.6 \) (or 60%)
Analysis of Options:
-
If you are a 10th grader, you are more likely to prefer pop.
- False: 67.8% prefer Hip-Hop vs. 32.1% prefer Pop.
-
If you like hip-hop, you are almost equally likely to be from 10th or 11th grade.
- Total Hip-Hop: 210 (112 from 10th and 98 from 11th)
- 10th: \( \frac{112}{210} \approx 0.533 \) (53.3%)
- 11th: \( \frac{98}{210} \approx 0.467 \) (46.7%)
- True, they are fairly close in proportions.
-
If you are an 11th grader, you are more likely to prefer hip-hop.
- False: 40% prefer Hip-Hop vs. 60% who prefer Pop.
-
If you like pop, you are more likely to be a 10th grader.
- Total Pop: 200 (53 from 10th and 147 from 11th)
- 10th: \( \frac{53}{200} \approx 0.265 \) (26.5%)
- 11th: \( \frac{147}{200} \approx 0.735 \) (73.5%)
- False: 73.5% of Pop fans are 11th graders.
Conclusion:
The statement that is true is "If you like hip-hop, you are almost equally likely to be from 10th or 11th grade."