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.
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.
