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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, each asked adult consumers the number of fiction paperbacks they had purchased the previous month. The results are below.

Publisher a
# of books Freq. Rel. Freq.
0 10
1 12
2 16
3 12
4 8
5 6
6 2
8 2
Publisher b
# of books Freq. Rel. Freq.
0 18
1 24
2 24
3 22
4 15
5 10
7 5
9 1
Publisher c
# of books Freq. Rel. Freq.
0-1 20
2-3 35
4-5 12
6-7 2
8-9 1
  • Find the relative frequencies for each survey. Write them in the charts.
  • 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 1. For Publisher C, make bar widths of 2.
  • In complete sentences, give two reasons why the graphs for Publishers A and B are not identical.
  • Would you have expected the graph for Publisher C to look like the other two graphs? Why or why not?
  • Make new histograms for Publisher A and Publisher B. This time, make bar widths of 2.
  • 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.
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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 on-board 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. Below is a summary of the bills for each group.

Singles
Amount($) Frequency Rel. Frequency
51-100 5
101-150 10
151-200 15
201-250 15
251-300 10
301-350 5
Couples
Amount($) 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
  • Fill in the relative frequency for each group.
  • Construct a histogram for the Singles group. Scale the x-axis by $50. widths. Use relative frequency on the y-axis.
  • Construct a histogram for the Couples group. Scale the x-axis by $50. Use relative frequency on the y-axis.
  • Compare the two graphs:
    • List two similarities between the graphs.
    • List two differences between the graphs.
    • Overall, are the graphs more similar or different?
  • 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.
  • Compare the graph for the Singles with the new graph for the Couples:
    • List two similarities between the graphs.
    • Overall, are the graphs more similar or different?
  • By scaling the Couples graph differently, how did it change the way you compared it to the Singles?
  • Based on the graphs, do you think that individuals spend the same amount, more or less, as singles as they do person by person in a couple? Explain why in one or two complete sentences.
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Refer to the following histograms and box plot. Determine which of the following are true and which are false. Explain your solution to each part in complete sentences.

Three graphs; the first is a histogram with a mode of 3 and fairly symmetrical distribution between 1 (minimum value) and 5 (maximum value); the second is a histogram with peaks at 1 (minimum value) and 5 (maximum value) with 3 having the lowest frequency; the third is a box plot with data between 0 and a value greater than 6, Q1 at 1, M at 3, and Q3 at 6.
  • The medians for all three graphs are the same.
  • We cannot determine if any of the means for the three graphs is different.
  • The standard deviation for (b) is larger than the standard deviation for (a).
  • We cannot determine if any of the third quartiles for the three graphs is different.
  • True
  • True
  • True
  • False
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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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