To analyze which observation is supported by the data, let's examine the most popular electives for both the juniors and seniors at Lawrence High School based on the given relative frequencies.
### Step-by-Step Solution:
1. Identify the relative frequencies for each elective among juniors:
- Art: [tex]\(0.02\)[/tex]
- Band: [tex]\(0.27\)[/tex]
- Choir: [tex]\(0.24\)[/tex]
- Drama: [tex]\(0.05\)[/tex]
2. Determine the most popular elective among juniors:
- The highest relative frequency among juniors is [tex]\(0.27\)[/tex] for Band.
3. Identify the relative frequencies for each elective among seniors:
- Art: [tex]\(0.12\)[/tex]
- Band: [tex]\(0.04\)[/tex]
- Choir: [tex]\(0.05\)[/tex]
- Drama: [tex]\(0.21\)[/tex]
4. Determine the most popular elective among seniors:
- The highest relative frequency among seniors is [tex]\(0.21\)[/tex] for Drama.
5. Compare these findings to the provided options:
- Option A. Choir is the most popular elective among seniors. - Incorrect (Drama is the most popular among seniors with [tex]\(0.21\)[/tex])
- Option B. Drama is the most popular elective among juniors. - Incorrect (Band is the most popular among juniors with [tex]\(0.27\)[/tex])
- Option C. Art is the most popular elective among seniors. - Incorrect (Drama is the most popular among seniors with [tex]\(0.21\)[/tex])
- Option D. Band is the most popular elective among juniors. - Correct (Band has the highest frequency among juniors with [tex]\(0.27\)[/tex])
Based on the data, the correct observation is:
D. Band is the most popular elective among juniors.
