Let's analyze the given two-way relative frequency table. The table shows the proportion of juniors and seniors at Lawrence High School who are enrolled in different fine arts electives:
\begin{tabular}{|c|c|c|c|c|c|}
\cline { 2 - 6 } \multicolumn{1}{c|}{} & Art & Band & Choir & Drama & Total \\
\hline Juniors & 0.02 & 0.27 & 0.24 & 0.05 & 0.58 \\
\hline Seniors & 0.12 & 0.04 & 0.05 & 0.21 & 0.42 \\
\hline Total & 0.14 & 0.31 & 0.29 & 0.26 & 1 \\
\hline
\end{tabular}
1. Determine the most popular elective among juniors:
- Art: 0.02
- Band: 0.27
- Choir: 0.24
- Drama: 0.05
The highest relative frequency for juniors is 0.27 for Band. Therefore, Band is the most popular elective among juniors.
2. Determine the most popular elective among seniors:
- Art: 0.12
- Band: 0.04
- Choir: 0.05
- Drama: 0.21
The highest relative frequency for seniors is 0.21 for Drama. Therefore, Drama is the most popular elective among seniors.
Based on the analysis:
- Option A: Choir is the most popular elective among seniors. (This is incorrect, Drama is the most popular elective among seniors.)
- Option B: Drama is the most popular elective among juniors. (This is incorrect, Band is the most popular elective among juniors.)
- Option C: Art is the most popular elective among seniors. (This is incorrect, Drama is the most popular elective among seniors.)
- Option D: Band is the most popular elective among juniors. (This is correct, Band has the highest relative frequency of 0.27 among juniors.)
Thus, the correct answer is:
D. Band is the most popular elective among juniors.
