## Practice with Data Representation

Complete these exercises and check your answers.

### Exercise

1. 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 |

**Table 2.62 Publisher A**

# of books | Freq. | Rel. Freq. |
---|---|---|

0 | 18 | |

1 | 24 | |

2 | 24 | |

3 | 22 | |

4 | 15 | |

5 | 10 | |

7 | 5 | |

9 | 1 |

**Table 2.63 Publisher B**

# of books | Freq. | Rel. Freq. |
---|---|---|

0–1 | 20 | |

2–3 | 35 | |

4–5 | 12 | |

6–7 | 2 | |

8–9 | 1 |

**Table 2.64 Publisher C**

- 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 one. For Publisher C, make bar widths of two.
- 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 two.
- 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.

2. 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 onboard 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. Following is a summary of the bills for each group.

Amount($) | Frequency | Rel. Frequency |
---|---|---|

51–100 | 5 | |

101–150 | 10 | |

151–200 | 15 | |

201–250 | 15 | |

251–300 | 10 | |

301–350 | 5 |

**Table 2.65 Singles**

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 |

**Table 2.66 Couples**

- 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 widths. 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?

- How did scaling the couples graph differently change the way you compared it to the singles graph?
- Based on the graphs, do you think that individuals spend the same amount, more or less, as singles as they do person by person as a couple? Explain why in one or two complete sentences.

3. 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**

- Construct a histogram of the data.
- Complete the columns of the chart.

*Use the following information to answer the next two exercises:* Suppose one hundred eleven people who shopped in a special t-shirt store were asked the number of t-shirts they own costing more than $19 each.

4. The percentage of people who own at most three t-shirts costing more than $19 each is approximately:

- 21
- 59
- 41
- Cannot be determined

5. If the data were collected by asking the first 111 people who entered the store, then the type of sampling is:

- cluster
- simple random
- stratified
- convenience

6. Following are the 2010 obesity rates by U.S. states and Washington, DC.

State | Percent (%) | State | Percent (%) | State | Percent (%) |
---|---|---|---|---|---|

Alabama | 32.2 | Kentucky | 31.3 | North Dakota | 27.2 |

Alaska | 24.5 | Louisiana | 31.0 | Ohio | 29.2 |

Arizona | 24.3 | Maine | 26.8 | Oklahoma | 30.4 |

Arkansas | 30.1 | Maryland | 27.1 | Oregon | 26.8 |

California | 24.0 | Massachusetts | 23.0 | Pennsylvania | 28.6 |

Colorado | 21.0 | Michigan | 30.9 | Rhode Island | 25.5 |

Connecticut | 22.5 | Minnesota | 24.8 | South Carolina | 31.5 |

Delaware | 28.0 | Mississippi | 34.0 | South Dakota | 27.3 |

Washington, DC | 22.2 | Missouri | 30.5 | Tennessee | 30.8 |

Florida | 26.6 | Montana | 23.0 | Texas | 31.0 |

Georgia | 29.6 | Nebraska | 26.9 | Utah | 22.5 |

Hawaii | 22.7 | Nevada | 22.4 | Vermont | 23.2 |

Idaho | 26.5 | New Hampshire | 25.0 | Virginia | 26.0 |

Illinois | 28.2 | New Jersey | 23.8 | Washington | 25.5 |

Indiana | 29.6 | New Mexico | 25.1 | West Virginia | 32.5 |

Iowa | 28.4 | New York | 23.9 | Wisconsin | 26.3 |

Kansas | 29.4 | North Carolina | 27.8 | Wyoming | 25.1 |

**Table 2.68**

Construct a bar graph of obesity rates of your state and the four states closest to your state. Hint: Label the *x*-axis with the states.

Source: Rice University, https://openstax.org/books/introductory-statistics/pages/2-homework

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