1. Copyright © 2014, 2011 Pearson Education, Inc. 1 Chapter 3 Describing Categorical Data

2. Copyright © 2014, 2011 Pearson Education, Inc. 2 3.1 Looking At Data Which hosts send the most visitors to Amazon’s Web site?  Data set consists of 188,996 visits  Host is a categorical variable  To answer this question we must describe the variation in Host

3. Copyright © 2014, 2011 Pearson Education, Inc. 3 3.1 Looking At Data Frequency and Relative Frequency Tables  The distribution of a categorical variable is a list of values with its associated count (frequency)  A frequency table summarizes the distribution of a categorical variable  A relative frequency table shows the proportion (or percentage) in each category

4. Copyright © 2014, 2011 Pearson Education, Inc. 4 3.1 Looking At Data

5. Copyright © 2014, 2011 Pearson Education, Inc. 5 3.2 Charts of Categorical Data Bar Charts and Pie Charts  Unless you need to know exact counts, charts are better than tables for summarizing more than five categories  The two most common displays of a categorical variable are a bar chart and a pie chart

6. Copyright © 2014, 2011 Pearson Education, Inc. 6 3.2 Charts of Categorical Data The Bar Chart  Uses horizontal or vertical bars to show the distribution of a categorical variable  Is called a Pareto chart when the categories are sorted by frequency (popular in quality control)  Becomes cluttered with too many categories  Is appropriate for ordinal categorical variables

7. Copyright © 2014, 2011 Pearson Education, Inc. 7 3.2 Charts of Categorical Data Bar Chart (Horizontal) of Top 10 Hosts

8. Copyright © 2014, 2011 Pearson Education, Inc. 8 3.2 Charts of Categorical Data Bar Chart (Vertical) of Top 10 Hosts

9. Copyright © 2014, 2011 Pearson Education, Inc. 9 3.2 Charts of Categorical Data The Pie Chart  Uses wedges of a circle to show the distribution of a categorical variable  Commonly chosen to illustrate market shares or sources of revenue for a company  Less useful than bar charts if we want to compare actual counts (easier to compare bars than angles of wedges)

10. Copyright © 2014, 2011 Pearson Education, Inc. 10 3.2 Charts of Categorical Data Pie Chart of Top 10 Hosts

11. Copyright © 2014, 2011 Pearson Education, Inc. 11 3.3 The Area Principle The Fundamental Rule for Data Displays  The area occupied by a part of the graph/chart that displays data should be proportional to the amount of data it represents  Charts decorated to attract attention often violate the area principle

12. Copyright © 2014, 2011 Pearson Education, Inc. 12 3.3 The Area Principle An Example Violating the Area Principle

13. Copyright © 2014, 2011 Pearson Education, Inc. 13 3.3 The Area Principle The Same Example Respecting the Area Principle

14. Copyright © 2014, 2011 Pearson Education, Inc. 14 4M Example 3.1: ROLLING OVER Motivation Are certain types of vehicles more prone to roll- over accidents than others?

15. Copyright © 2014, 2011 Pearson Education, Inc. 15 4M Example 3.1: ROLLING OVER Method Data gathered from Fatality Analysis Reporting System (FARS) for roll-over accidents on interstate highways. Cases that make up the rows are accidents resulting in roll-overs in 2000. The column of interest is model of the car involved.

16. Copyright © 2014, 2011 Pearson Education, Inc. 16 4M Example 3.1: ROLLING OVER Mechanics

17. Copyright © 2014, 2011 Pearson Education, Inc. 17 4M Example 3.1: ROLLING OVER Mechanics

18. Copyright © 2014, 2011 Pearson Education, Inc. 18 4M Example 3.1: ROLLING OVER Message Ford Broncos were involved in more than twice as many roll-over accidents as the next-closest model.

19. Copyright © 2014, 2011 Pearson Education, Inc. 19 4M Example 3.2: SELLING SMARTPHONES TO BUSINESSES Motivation Apple, Google and Research in Motion (RIM) aggressively compete to sell their smartphones to businesses. RIM has dominated with its Blackberry line, but has that success held up to the intense competition from Apple and Google?

20. Copyright © 2014, 2011 Pearson Education, Inc. 20 4M Example 3.2: SELLING SMARTPHONES TO BUSINESSES Method

21. Copyright © 2014, 2011 Pearson Education, Inc. 21 4M Example 3.2: SELLING SMARTPHONES TO BUSINESSES Mechanics

22. Copyright © 2014, 2011 Pearson Education, Inc. 22 4M Example 3.2: SELLING SMARTPHONES TO BUSINESSES Mechanics

23. Copyright © 2014, 2011 Pearson Education, Inc. 23 4M Example 3.2: SELLING SMARTPHONES TO BUSINESSES Message Corporate customers are purchasing more iPhones and Android phones for managers. From 2010 to 2011, Blackberry sales grew less than sales of iPhones and Android phones. While RIM still had the largest share of the market in 2011, it had decreased to less than 50%.

24. Copyright © 2014, 2011 Pearson Education, Inc. 24 3.4 Mode and Median Mode  Category with the highest frequency  The longest bar in a bar chart  The widest slice in a pie chart  Two or more categories can tie with the highest frequency (bimodal or multimodal)

25. Copyright © 2014, 2011 Pearson Education, Inc. 25 3.4 Mode and Median Median  Not appropriate for nominal data  Data must be ordinal  It is the category label of the middle observation in ordered data

26. Copyright © 2014, 2011 Pearson Education, Inc. 26 Best Practices  Use a bar chart to show the frequencies of a categorical variable.  Use a pie chart to show the proportions of a categorical variable.  Keep the baseline of a bar chart at zero.  Preserve the ordering of an ordinal variable.

27. Copyright © 2014, 2011 Pearson Education, Inc. 27 Best Practices (Continued)  Respect the area principle.  Show the best plots to answer the motivating question.  Label your chart to show the categories and indicate whether some have been combined or omitted.

28. Copyright © 2014, 2011 Pearson Education, Inc. 28 Pitfalls  Avoid elaborate plots that may be deceptive.  Do not show too many categories.  Do not put ordinal data in a pie chart.  Do not carelessly round data.