Question

6. The researcher can choose how wide a bin of a histogram can be-True or false?

16. 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

Publisher A

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

  Publisher B

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

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.

18. 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.

Answer 1

6. TRUE, researchers can choose the bin of histogram.

16. (a) Relative frequency is calculated by dividing the frequency value by the total frequency.

PUBLISHER A
# of books	Freq.	Rel. Freq.
0	10	14.7%
1	12	17.6%
2	16	23.5%
3	12	17.6%
4	8	11.8%
5	6	8.8%
6	2	2.9%
8	2	2.9%
sum:	68

PUBLISHER B
# of books	Freq.	Rel. Freq.
0	18	15.1%
1	24	20.2%
2	24	20.2%
3	22	18.5%
4	15	12.6%
5	10	8.4%
7	5	4.2%
9	1	0.8%
sum:	119

PUBLISHER C
# of books	Freq.	Rel. Freq.
0–1	20	28.6%
2–3	35	50.0%
4–5	12	17.1%
6–7	2	2.9%
8–9	1	1.4%
sum:	70

(b)

(c) Publishers A and B have different graphs because

1. The consumer sample that the 2 publishers surveyed would be different
2. The consumers responded differently for last month's purchases and each graph has a window of only 1 bar width that increases the variability

(d) No, graph for publisher C would look different from the other two graphs because of the different window size. Variance is decreased in publisher C graph as compared to the other 2 graphs.

(e)

(f) The new graphs for publisher C are more similar to the new graphs of publisher A and B because of the new bar width used. The interval 2 is able to decrease the variance and spread and hence they look more similar.

18. (a) Histogram:

(b) Calculating relative frequency and cumulative relative frequency for completing the columns of chart: