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Practice with Data Representation

Site: Saylor Academy
Course: GKT101: General Knowledge for Teachers – Math
Book: Practice with Data Representation
Printed by: Guest user
Date: Thursday, 3 April 2025, 6:08 PM

Description

Complete these exercises and check your answers.

Table of contents

Exercise

1. Suppose that three book publishers were interested in the number of fiction paperbacks adult consumers purchase per month. Each publisher conducted a survey. In the survey, adult consumers were asked the number of fiction paperbacks they had purchased the previous month. The results are as follows:

# of books Freq. Rel. Freq.
0 10  
1 12  
2 16  
3 12  
4 8  
5 6  
6 2  
8 2  
Table 2.62 Publisher A

# of books Freq. Rel. Freq.
0 18  
1 24  
2 24  
3 22  
4 15  
5 10  
7 5  
9 1  
Table 2.63 Publisher B

# of books Freq. Rel. Freq.
0–1 20  
2–3 35  
4–5 12  
6–7 2  
8–9 1  
Table 2.64 Publisher C

  1. Find the relative frequencies for each survey. Write them in the charts.
  2. Using either a graphing calculator, computer, or by hand, use the frequency column to construct a histogram for each publisher's survey. For Publishers A and B, make bar widths of one. For Publisher C, make bar widths of two.
  3. In complete sentences, give two reasons why the graphs for Publishers A and B are not identical.
  4. Would you have expected the graph for Publisher C to look like the other two graphs? Why or why not?
  5. Make new histograms for Publisher A and Publisher B. This time, make bar widths of two.
  6. Now, compare the graph for Publisher C to the new graphs for Publishers A and B. Are the graphs more similar or more different? Explain your answer.
2. Often, cruise ships conduct all on-board transactions, with the exception of gambling, on a cashless basis. At the end of the cruise, guests pay one bill that covers all onboard transactions. Suppose that 60 single travelers and 70 couples were surveyed as to their on-board bills for a seven-day cruise from Los Angeles to the Mexican Riviera. Following is a summary of the bills for each group.

Amount($) Frequency Rel. Frequency
51–100 5  
101–150 10  
151–200 15  
201–250 15  
251–300 10  
301–350 5  
Table 2.65 Singles

Amount($) Frequency Rel. Frequency
100–150 5  
201–250 5  
251–300 5  
301–350 5  
351–400 10  
401–450 10  
451–500 10  
501–550 10  
551–600 5  
601–650 5  
Table 2.66 Couples

  1. Fill in the relative frequency for each group.
  2. Construct a histogram for the singles group. Scale the x-axis by $50 widths. Use relative frequency on the y-axis.
  3. Construct a histogram for the couples group. Scale the x-axis by $50 widths. Use relative frequency on the y-axis.
  4. Compare the two graphs:
    1. List two similarities between the graphs.
    2. List two differences between the graphs.
    3. Overall, are the graphs more similar or different?
  5. Construct a new graph for the couples by hand. Since each couple is paying for two individuals, instead of scaling the x-axis by $50, scale it by $100. Use relative frequency on the y-axis.
  6. Compare the graph for the singles with the new graph for the couples:
    1. List two similarities between the graphs.
    2. Overall, are the graphs more similar or different?
  7. How did scaling the couples graph differently change the way you compared it to the singles graph?
  8. Based on the graphs, do you think that individuals spend the same amount, more or less, as singles as they do person by person as a couple? Explain why in one or two complete sentences.
3. Twenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follows.

# of movies Frequency Relative Frequency Cumulative Relative Frequency
0 5    
1 9    
2 6    
3 4    
4 1    
Table 2.67

  1. Construct a histogram of the data.
  2. Complete the columns of the chart.

Use the following information to answer the next two exercises: Suppose one hundred eleven people who shopped in a special t-shirt store were asked the number of t-shirts they own costing more than $19 each.

4. The percentage of people who own at most three t-shirts costing more than $19 each is approximately:
  1. 21
  2. 59
  3. 41
  4. Cannot be determined
5.  If the data were collected by asking the first 111 people who entered the store, then the type of sampling is:
  1. cluster
  2. simple random
  3. stratified
  4. convenience
6. Following are the 2010 obesity rates by U.S. states and Washington, DC.

State Percent (%) State Percent (%) State Percent (%)
Alabama 32.2 Kentucky 31.3 North Dakota 27.2
Alaska 24.5 Louisiana 31.0 Ohio 29.2
Arizona 24.3 Maine 26.8 Oklahoma 30.4
Arkansas 30.1 Maryland 27.1 Oregon 26.8
California 24.0 Massachusetts 23.0 Pennsylvania 28.6
Colorado 21.0 Michigan 30.9 Rhode Island 25.5
Connecticut 22.5 Minnesota 24.8 South Carolina 31.5
Delaware 28.0 Mississippi 34.0 South Dakota 27.3
Washington, DC 22.2 Missouri 30.5 Tennessee 30.8
Florida 26.6 Montana 23.0 Texas 31.0
Georgia 29.6 Nebraska 26.9 Utah 22.5
Hawaii 22.7 Nevada 22.4 Vermont 23.2
Idaho 26.5 New Hampshire 25.0 Virginia 26.0
Illinois 28.2 New Jersey 23.8 Washington 25.5
Indiana 29.6 New Mexico 25.1 West Virginia 32.5
Iowa 28.4 New York 23.9 Wisconsin 26.3
Kansas 29.4 North Carolina 27.8 Wyoming 25.1
Table 2.68


Construct a bar graph of obesity rates of your state and the four states closest to your state. Hint: Label the x-axis with the states.


Source: Rice University, https://openstax.org/books/introductory-statistics/pages/2-homework
Creative Commons License This work is licensed under a Creative Commons Attribution 4.0 License.

Answers

2.
Amount($) Frequency Relative Frequency
51–100 5 0.08
101–150 10 0.17
151–200 15 0.25
201–250 15 0.25
251–300 10 0.17
301–350 5 0.08
Table 2.86 Singles

Amount($) Frequency Relative Frequency
100–150 5 0.07
201–250 5 0.07
251–300 5 0.07
301–350 5 0.07
351–400 10 0.14
401–450 10 0.14
451–500 10 0.14
501–550 10 0.14
551–600 5 0.07
601–650 5 0.07
Table 2.87 Couples

  1. See Table 2.86 and Table 2.87.
  2. In the following histogram data values that fall on the right boundary are counted in the class interval, while values that fall on the left boundary are not counted (with the exception of the first interval where both boundary values are included).

    Figure 2.59
  3. In the following histogram, the data values that fall on the right boundary are counted in the class interval, while values that fall on the left boundary are not counted (with the exception of the first interval where values on both boundaries are included).

    Figure 2.60
  4. Compare the two graphs:
    1. Answers may vary. Possible answers include:
      • Both graphs have a single peak.
      • Both graphs use class intervals with width equal to $50.
    2. Answers may vary. Possible answers include:
      • The couples graph has a class interval with no values.
      • It takes almost twice as many class intervals to display the data for couples.
    3. Answers may vary. Possible answers include: The graphs are more similar than different because the overall patterns for the graphs are the same.
  5. Check student's solution.
  6. Compare the graph for the Singles with the new graph for the Couples:
      • Both graphs have a single peak.
      • Both graphs display 6 class intervals.
      • Both graphs show the same general pattern.
    2. Answers may vary. Possible answers include: Although the width of the class intervals for couples is double that of the class intervals for singles, the graphs are more similar than they are different.
  7. Answers may vary. Possible answers include: You are able to compare the graphs interval by interval. It is easier to compare the overall patterns with the new scale on the Couples graph. Because a couple represents two individuals, the new scale leads to a more accurate comparison.
  8. Answers may vary. Possible answers include: Based on the histograms, it seems that spending does not vary much from singles to individuals who are part of a couple. The overall patterns are the same. The range of spending for couples is approximately double the range for individuals.
4. c
6.  Answers will vary.