Question

The following table shows the number of hours some high school students in two towns spend watching TV each week:

Town A
16
25
42
38
17
32
42
10
17
Town B
8
0
0
17
30
8
21
9
19


Part A: Create a five-number summary and calculate the interquartile range for the two sets of data. (6 points)

Part B: Are the box plots symmetric? Justify your answer. (4 points)

Answer 1

The first step is to put the data in order, as shown in the diagram below

Five summaries of Town A
Lowest Value = 10
Lower Quartile, $Q_{1}$ = 16.5 (The value falls between 16 and 17)
Median, $Q_{2}$ = 25
Upper Quartile, $Q_{3}$ = 40 (The middle value between 38 and 42)
Highest value = 42

Five summaries of Town B
Lowest value = 0
Lower Quartile, $Q_{1}$ = 4 (The middle value between 0 and 8)
Median, $Q_{2}$ = 9
Upper Quartile, $Q_{3}$ = 20 (The middle value between 19 and 21)
Highest Value = 30

The box plot for two towns is shown in the diagram below. 
Town A box plot is not symmetrical, it's tailing on the left
Town B box plot is not symmetrical, it's tailing on the right

Answer 2

Five-number summary for Town A: 10, 16.5, 25, 40, 42

For Town B: 0, 4, 9, 20, 30

Town A IQR: 23.5

Town B IQR: 16

Their box plots are not symmetric

What is the Five-Number Summary?

The five-number summary comprises of:

• Min and max values
• Median
• Lower and Upper Quartile

A box plot displays the five-number summary. If a box plot is symmetric, the median will be at the middle of the rectangular box, and the whiskers will be of almost the same length.

Five-number Summary for Town A, 16, 25, 42, 38, 17, 32, 42, 10, 17:

• Minimum: 10
• First Quartile: 16.5
• Median: 25
• Third Quartile: 40
• Maximum: 42

Interquartile range for Town A = 40 - 16.5 = 23.5

Five-number Summary for Town B, 8, 0, 0, 17, 30, 8, 21, 9, 19:

• Minimum: 0
• First Quartile: 4
• Median: 9
• Third Quartile: 20
• Maximum: 30

Interquartile range for Town B = 20 - 4 = 16.

Part B: The box plots for Town A and town B are in the image attached below.

Both box plots are not symmetrical because their whiskers have varying length and their medians are not in the middle of the rectangular box.

Learn more about five-number summary on:

https://brainly.com/question/24809873