Statistics for business decision making and analysis robert stine and foster chapter 03

Chapter Describing Categorical Data Copyright © 2011 Pearson Education, Inc 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 of 28 Copyright © 2011 Pearson Education, Inc 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 of 28 Copyright © 2011 Pearson Education, Inc 3.1 Looking At Data of 28 Copyright © 2011 Pearson Education, Inc 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 of 28 Copyright © 2011 Pearson Education, Inc 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 of 28 Copyright © 2011 Pearson Education, Inc 3.2 Charts of Categorical Data Bar Chart (Horizontal) of Top 10 Hosts of 28 Copyright © 2011 Pearson Education, Inc 3.2 Charts of Categorical Data Bar Chart (Vertical) of Top 10 Hosts of 28 Copyright © 2011 Pearson Education, Inc 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 of 28 Copyright © 2011 Pearson Education, Inc 3.3 The Area Principle The Same Example Respecting the Area Principle 14 of 28 Copyright © 2011 Pearson Education, Inc 4M Example 3.1: ROLLING OVER Motivation Are certain types of vehicles more prone to rollover accidents than others? 15 of 28 Copyright © 2011 Pearson Education, Inc 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 of 28 Copyright © 2011 Pearson Education, Inc 4M Example 3.1: ROLLING OVER Mechanics 17 of 28 Copyright © 2011 Pearson Education, Inc 4M Example 3.1: ROLLING OVER Mechanics 18 of 28 Copyright © 2011 Pearson Education, Inc 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 of 28 Copyright © 2011 Pearson Education, Inc 4M Example 3.2: CHIP SALES Motivation Infineon pled guilty to price fixing for DRAM’s in September 2004 Did Infineon gain a larger share of the market for chips during this period? 20 of 28 Copyright © 2011 Pearson Education, Inc 4M Example 3.2: CHIP SALES Method 21 of 28 Copyright © 2011 Pearson Education, Inc 4M Example 3.2: CHIP SALES Mechanics 22 of 28 Copyright © 2011 Pearson Education, Inc 4M Example 3.2: CHIP SALES Message Infineon and Samsung increased their shares from 1999 to 2002 It appears to have been at the expense of smaller companies 23 of 28 Copyright © 2011 Pearson Education, Inc 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) 24 of 28 Copyright © 2011 Pearson Education, Inc 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 25 of 28 Copyright © 2011 Pearson Education, Inc 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  Preserve the ordering of an ordinal variable 26 of 28 Copyright © 2011 Pearson Education, Inc 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 27 of 28 Copyright © 2011 Pearson Education, Inc 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 28 of 28 Copyright © 2011 Pearson Education, Inc ... Education, Inc 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... Education, Inc 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... CHIP SALES Motivation Infineon pled guilty to price fixing for DRAM’s in September 2004 Did Infineon gain a larger share of the market for chips during this period? 20 of 28 Copyright © 2011 Pearson