Question

robin collected data on the number of hours she watched television on sunday through thursday nights for a period of 3 weeks. the data are shown in the table below. using an appropriate scale on the number line below, construct a box plot for the 15 values.

Explanation:

Step1: List all data points

First, we list all the 15 data points from the table:
Week 1: \( 4, 3, 3.5, 2, 2 \)
Week 2: \( 4.5, 5, 2.5, 3, 1.5 \)
Week 3: \( 4, 3, 1, 1.5, 2.5 \)
Combined data: \( 1, 1.5, 1.5, 2, 2, 2.5, 2.5, 3, 3, 3, 3.5, 4, 4, 4.5, 5 \)

Step2: Find the minimum and maximum

Minimum value (\( \text{min} \)): \( 1 \)
Maximum value (\( \text{max} \)): \( 5 \)

Step3: Find the median (Q2)

Since there are 15 data points (odd number), the median is the 8th value when sorted. From the sorted data, the 8th value is \( 3 \), so \( \text{Q2} = 3 \)

Step4: Find Q1 (median of lower half)

The lower half of the data (first 7 values: \( 1, 1.5, 1.5, 2, 2, 2.5, 2.5 \))
Median of lower half: the 4th value, which is \( 2 \), so \( \text{Q1} = 2 \)

Step5: Find Q3 (median of upper half)

The upper half of the data (last 7 values: \( 3, 3, 3.5, 4, 4, 4.5, 5 \))
Median of upper half: the 4th value, which is \( 4 \), so \( \text{Q3} = 4 \)

Step6: Construct the box plot

• Draw a number line from \( 0 \) to \( 6 \) (appropriate scale).
• Plot the minimum (\( 1 \)) and maximum (\( 5 \)) as the endpoints of the whiskers.
• Draw a box from \( \text{Q1} = 2 \) to \( \text{Q3} = 4 \), with a line inside the box at \( \text{Q2} = 3 \) (the median).

Answer:

The box plot has:

• Minimum: \( 1 \)
• Q1: \( 2 \)
• Median (Q2): \( 3 \)
• Q3: \( 4 \)
• Maximum: \( 5 \)

To construct the box plot:

1. Mark \( 1 \) (min) and \( 5 \) (max) on the number line.
2. Draw a box from \( 2 \) (Q1) to \( 4 \) (Q3).
3. Draw a vertical line inside the box at \( 3 \) (median).