Question

1. mr. alven took a poll of his 30 students. he asked their hourly pay rate.

seniors: 10, 9.50, 8, 11, 12, 10
sophomores: 7.50, 8, 10, 7.50, 8, 8
create a box-and-whisker plot. which group of students had the higher hourly pay rate? do seniors make more money?

Explanation:

Step1: Organize Seniors' Data

Sort seniors' pay rates: \(8, 9.50, 10, 10, 11, 12\)

• Minimum: \(8\)
• Q1: Median of lower half (\(8, 9.50\)): \(\frac{8 + 9.50}{2}=8.75\)
• Median (Q2): Median of \(8, 9.50, 10, 10, 11, 12\): \(\frac{10 + 10}{2}=10\)
• Q3: Median of upper half (\(11, 12\)): \(\frac{11 + 12}{2}=11.5\)
• Maximum: \(12\)

Step2: Organize Sophomores' Data

Sort sophomores' pay rates: \(7.50, 7.50, 8, 8, 8, 10\)

• Minimum: \(7.50\)
• Q1: Median of lower half (\(7.50, 7.50\)): \(7.50\)
• Median (Q2): Median of \(7.50, 7.50, 8, 8, 8, 10\): \(\frac{8 + 8}{2}=8\)
• Q3: Median of upper half (\(8, 10\)): \(\frac{8 + 10}{2}=9\)
• Maximum: \(10\)

Step3: Compare Distributions

Seniors' data (min=8, Q1=8.75, median=10, Q3=11.5, max=12) has higher values overall than sophomores' (min=7.50, Q1=7.50, median=8, Q3=9, max=10). The median, Q1, Q3, and max of seniors are greater than those of sophomores.

Answer:

Seniors had the higher hourly pay rate. To create box - and - whisker plots:

• For Seniors: Plot with minimum \(8\), Q1 \(8.75\), median \(10\), Q3 \(11.5\), maximum \(12\).
• For Sophomores: Plot with minimum \(7.50\), Q1 \(7.50\), median \(8\), Q3 \(9\), maximum \(10\).