Section 1.2 Exercises

For Exercise 1.15, see page 9; for 1.16 and 1.17, see page 10, for 1.18 and 1.19, see pages 11-12; for 1.20 and 1.21, see page 15; for 1.22 and 1.23, see page 19; and for 1.24, see page 20.

Question 1.25

1.25 Which graphical display should you use?

For each of the following scenarios, decide which graphical display (pie chart, bar graph, Pareto chart, stemplot, or histogram) you would use to describe the distribution of the variable. Give a reason for your choice and if there is an alternative choice that would also be reasonable, explain why your choice was better than the alternative.

  1. The amounts of the 3278 sales that your company made last month.
  2. You did a survey of your customers and asked them to select the characteristic of your company that they like the best. They can select from a list of seven characteristics. You have 342 responses.
  3. The starting salaries of the 15 people who graduated from your college with the same major as you.
  4. Your customers are businesses who have been classified into eight groups based on the size of their business and the amount of sales that your company has with them. You have the counts for each group.

1.25

(a) Histogram would be best to show the distribution. (b) Pareto chart would be the best to prioritize those characteristics that they liked best; pie chart might also be suitable. (c) A stemplot would be best because it is a small dataset; a histogram might also be suitable. (d) Pie chart is likely best in this situation to divide all the customers into groups from the whole; a Pareto or bar graph might also be suitable.

Question 1.26

1.26 Garbage is big business.

The formal name for garbage is “municipal solid waste.” In the United States, approximately 250 million tons of garbage are generated in a year. Following is a breakdown of the materials that made up American municipal solid waste in 2012.11

garbage

Material Weight (million tons) Percent of total
Food scraps 36.4 14.5
Glass 11.6 4.6
Metals 22.4 8.9
Paper, paperboard 68.6 27.4
Plastics 31.7 12.7
Rubber, leather 7.5 3.0
Textiles 14.3 5.7
Wood 15.8 6.3
Yard trimmings 34.0 13.5
Other 8.5 3.4
Total 250.9 100.0
  1. Add the weights. The sum is not exactly equal to the value of 250.9 million tons given in the table. Why?
  2. Make a bar graph of the percents. The graph gives a clearer picture of the main contributors to garbage if you order the bars from tallest to shortest.
  3. Also make a pie chart of the percents. Comparing the two graphs, notice that it is easier to see the small differences among “Food scraps,” “Plastics,” and ”Yard trimmings” in the bar graph.

Question 1.27

1.27 Market share for desktop browsers

The following table gives the market share for the major search engines.12

browser

22

Search engine Market share
Internet Explorer 58.2%
Chrome 17.7%
Firefox 16.8%
Safari 5.7%
Opera 1.2%
Other 0.4%
  1. Use a bar graph to display the market shares.
  2. Summarize what the graph tells you about market shares for desktop browsers.

1.27

(b) Internet Explorer has by far the largest percentage of market share, followed by Chrome and Firefox. Other browsers have very little market share.

Question 1.28

1.28 Reliability of household appliances.

You are writing an article for a consumer magazine based on a survey of the magazine’s readers. Of 13,376 readers who reported owning Brand A dishwashers, 2942 required a service call during the past year. Only 192 service calls were reported by the 480 readers who owned Brand B dishwashers.

  1. Why is the count of service calls (2942 versus 192) not a good measure of the reliability of these two brands of dishwashers?
  2. Use the information given to calculate a suitable measure of reliability. What do you conclude about the reliability of Brand A and Brand B?

Question 1.29

1.29 Your Facebook app can generate a million dollars a month.

A report on Facebook suggests that Facebook apps can generate large amounts of money, as much as $1 million a month.13 The following table gives the numbers of Facebook users by country for the top 10 countries based on the number of users. It also gives the increases in the number of Facebook users for the one-month period from May 15, 2014, to June 15, 2014.14

facebk

Country Facebook users (in millions)
Brazil 29.30
India 37.38
Mexico 29.80
Germany 21.46
France 23.19
Philippines 26.87
Indonesia 40.52
United Kingdom 30.39
United States 155.74
Turkey 30.63
  1. Use a bar graph to describe the numbers of users in these countries.
  2. Do you think that the United States is an outlier in this data set? Explain your answer.
  3. Describe the major features of your graph in a short paragraph.

1.29

(b) The United States is a clear outlier. They have 4 or 5 times as many Facebook users as the other countries, despite having a population smaller than some of the other countries. (c) The United States dominates; many other countries shown have similar amounts of Facebook users.

Question 1.30

1.30 Facebook use increases by country.

Refer to the previous exercise. Here are the data for the increases in the number of Facebook users for the one-month period from May 15, 2014, to June 15, 2014.

facebk

Country Increase in users (in millions)
Brazil 2.47
India 1.75
Mexico 0.84
Germany 0.51
France 0.38
Philippines 0.38
Indonesia 0.37
United Kingdom 0.22
United States 0.65
Turkey 0.09
  1. Use a bar graph to describe the increase in users in these countries.
  2. Describe the major features of your graph in a short paragraph.
  3. Do you think a stemplot would be a better graphical display for these data? Give reasons for your answer.
  4. Write a short paragraph about possible business opportunities suggested by the data you described in this exercise and the previous one.

Question 1.31

1.31 Products for senior citizens.

The market for products designed for senior citizens in the United States is expanding. Here is a stemplot of the percents of residents aged 65 and older in the 50 states for 2012 as estimated by the U.S. Census Bureau American Community Survey.15 The stems are whole percents, and the leaves are tenths of a percent. Describe the shape, center, and spread of this distribution.

us65

8 5
9 5
10 9
11 58
12 1
13 00000222566788
14 0111134455567778889
15 0113478
16 08
17 0
18 2

1.31

The shape is symmetric, the center is around 14. The range is between 8.5 and 18.2.

23

Question 1.32

1.32 The Canadian market.

Refer to Exercise 1.31. Here are similar data for the 13 Canadian provinces and territories:16

canadap

Province/territory Percent over 65
Alberta 11.1
British Columbia 15.7
Manitoba 14.3
New Brunswick 16.5
Newfoundland and Labrador 16.0
Northwest Territories 5.8
Nova Scotia 16.6
Nunavut 3.3
Ontario 14.6
Prince Edward Island 16.3
Quebec 15.9
Saskatchewan 14.9
Yukon 9.1
  1. Display the data graphically, and describe the major features of your plot.
  2. Explain why you chose the particular format for your graphical display. What other types of graph could you have used? What are the strengths and weaknesses of each for displaying this set of data?