Histograms, Frequency Polygons, and Time Series Graphs · Exercise 12

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:

$$\begin{array}{ccc}\text{Number of Books}& \text{Frequency}& \text{Relative Frequency}\\ \text{0}& \text{10}& \\ \text{1}& \text{12}& \\ \text{2}& \text{16}& \\ \text{3}& \text{12}& \\ \text{4}& \text{8}& \\ \text{5}& \text{6}& \\ \text{6}& \text{2}& \\ \text{8}& \text{2}& \end{array}$$

$$\begin{array}{ccc}\text{Number of Books}& \text{Frequency}& \text{Relative Frequency}\\ \text{0}& \text{18}& \\ \text{1}& \text{24}& \\ \text{2}& \text{24}& \\ \text{3}& \text{22}& \\ \text{4}& \text{15}& \\ \text{5}& \text{10}& \\ \text{7}& \text{5}& \\ \text{9}& \text{1}& \end{array}$$

$$\begin{array}{ccc}\text{Number of Books}& \text{Frequency}& \text{Relative Frequency}\\ \text{0–1}& \text{20}& \\ \text{2–3}& \text{35}& \\ \text{4–5}& \text{12}& \\ \text{6–7}& \text{2}& \\ \text{8–9}& \text{1}& \end{array}$$

(a) Find the relative frequencies for each survey. Write them in the charts.
(b) Using either a graphing calculator or 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.
(c) In complete sentences, give two reasons why the graphs for Publishers A and B are not identical.
(d) Would you have expected the graph for Publisher C to look like the other two graphs? Why or why not?
(e) Make new histograms for Publisher A and Publisher B. This time, make bar widths of 2.
(f) 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.

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Statistics · §2.2 Histograms, Frequency Polygons, and Time Series Graphs · Exercise 12