<< Chapter < Page Chapter >> Page >

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.

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.

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

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Collaborative statistics (with edits: teegarden). OpenStax CNX. Jul 20, 2009 Download for free at http://legacy.cnx.org/content/col10561/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Collaborative statistics (with edits: teegarden)' conversation and receive update notifications?

Ask