1Chapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.Chapter 3 Displaying and Describing Categorical DataChapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.2Types of Univariate Categorical Displays Frequency and Relative Frequency Table Bar Chart Pareto Chart Pie ChartChapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.3Frequency Tables The name of each category, and the number of observations in each category.Chapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.4Relative Frequency Tables Similar, but gives the percentages (instead of counts) for each category.Chapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.5Relative Frequency vs. Percentage The table on the previous page may be called a “relative frequency” table, but it is displaying percentages, not relative frequencies. Percentages will range from 0 to 100% Relative frequencies will range from 0 to 1.00ClassFrequencyRelative Frequency%First 325 0.1477 14.77Second 285 0.1295 12.95Third 706 0.3208 32.08Crew 885 0.4021 40.21Total 2201 1.000 100.0Chapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.6Frequency Bar Chart A graphical display of the data in a frequency table.Chapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.7Relative Frequency Bar Chart A graphical display of the data in a relativefrequency table.Chapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.8Output from JMP Software It is possible to get JMP software to display the frequency or the relative frequency bar chart.Chapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.9Pareto Chart A bar chart with the bars put in order from the most frequently occurring category on the left to least frequently occurring category on the right is called a Pareto Chart. Typically a Pareto Chart has a frequency scale on the left and a relative frequency scale on the right. Sometimes a Pareto Chart contains a line above the bars indicating cumulative frequency and cumulative relative frequency.Chapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.10http://en.wikipedia.org/wiki/Pareto_chart168 Late Arrivals to Work Example Pareto ChartChapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.11 Another common method of displaying categorical data:Pie ChartsChapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.12Pie Charts from JMP Both frequency and relative frequency pie charts can be generated. JMPs pie charts are designed to be presented in color (i.e., which slice is which category is difficult to determine in black and white).Chapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.13What’s Wrong Here? This pie chart of the percentage of high-school students who engage in specified dangerous behaviors has a problem. Can you see it?Chapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.14Types of Bivariate Categorical Data Displays Contingency Tables Side by Side Pie Charts Segmented Bar Charts Mosaic PlotChapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.15Contingency Tables A contingency table allows us to look at two categorical variables together. Example: we can examine the class of ticket and whether a person survived the Titanic:Chapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.16Contingency Tables (cont.) Each cell of the table gives the count for a combination of values of the two variables.Chapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.17Contingency Tables (cont.) The margins of the table, both on the right and on the bottom, give totals and the frequency distributions for each of the variables. Each frequency distribution is called a marginal distribution of its respective variable. The marginal distribution of Survival is:Chapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.18Contingency Tables (cont.) The marginal distribution of Class is:Chapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.19Conditional Distributions A conditional distribution shows the distribution of one variable for just the individuals who satisfy some condition on another variable. The following is the conditional distribution of Survival, conditional on having been a crew member:24%76%100%Chapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.20Conditional Distributions (cont.) The following is the conditional distribution of ticket Class, conditional on having survived:28.6%16.6%25.0%29.8%100%Chapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.21Conditional Distributions (cont.) The following is the conditional distribution of ticket Class, conditional on having died:8.2%11.2%35.4%45.2%100%Chapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.22Conditional Distributions (cont.) These last two conditional distributions tell us that there is a difference in class for those who survived and those who perished. This can be shown with pie charts of the two distributions: FirstFirstSecondThirdThirdCrewCrewChapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.23Conditional Distributions (cont.) We see that the distribution of Class for the survivors is different from that of the nonsurvivors. This leads us to believe that Class and Survivalare associated, that they are not independent. The variables would be considered independent when the distribution of one variable in a contingency table is the same for all categories of the other variable.Chapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.24Segmented Bar Charts A segmented bar chartdisplays the same information as a pie chart, but in the form of bars instead of circles.SecondSecondFirstFirstThirdThirdCrewCrewChapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.25Class Activity – Groups of 2 (or 3) 200 adults shopping at a supermarket were asked about the highest level of education they had completed and whether or not they smoke cigarettes. Results are summarized in the table on the next page. Is there an association between education level and smoking?Chapter03 Presentation 1213Copyright © 2009 Pearson Education, Inc.26Class Activity To help you answer the question on the
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