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# JMF-2-07 - Descriptive Statistics Chapter 2 Notes Set 2...

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CH Reilly UCF - IEMS - STA 3032 1 Descriptive Statistics Chapter 2 Notes Set 2 Spring 2007

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CH Reilly UCF - IEMS - STA 3032 2 Not all data are created equal Some data are quantitative. Example: Average miles per gallon for each of our cars. Some data are qualitative or categorical. Example: The makes of our cars. We will summarize and analyze different types of data differently. Unfortunately, it is not unusual for some people to treat qualitative data as quantitative data. (Example: course evaluations.)
CH Reilly UCF - IEMS - STA 3032 3 Qualitative or categorical data Tabular representation. Frequencies by category (counts). Relative frequencies by category (proportions). Graphical representation. Bar charts (absolute or relative frequency – depends on how axis is labeled). Pie charts. Pareto diagram – bar chart with bars in decreasing order of height. Helpful for identifying root causes of problems.

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CH Reilly UCF - IEMS - STA 3032 4 Example – M&M’s (764) Color Frequency Rel. Freq. Cumulative Brown 249 0.326 0.326 Red 177 0.232 0.558 Yellow 121 0.158 0.716 Green 96 0.126 0.842 Orange 83 0.108 0.950 Blue 38 0.050 1.000
CH Reilly UCF - IEMS - STA 3032 5 Example (cont’d.) – Pareto (bar) chart M&M's by Color 0 100 200 300 Brown Red Yellow Green Orange Blue Color Count

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CH Reilly UCF - IEMS - STA 3032 6 Comments on categories In this example, the categories happen to be ordered according to decreasing frequency. Many times, there is not one correct sequencing of the categories (except for a Pareto chart). A counterexample, however, is customer satisfaction surveys. The sequencing of “excellent”, “good”, “fair”, and “poor” is fairly straightforward.
CH Reilly UCF - IEMS - STA 3032 7 Example (cont’d.) – Pie Chart M&M's by Color Brown Red Yellow Green Orange Blue

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CH Reilly UCF - IEMS - STA 3032 8 Which type of presentation is better? It depends on who the audience is. Some people, including yours truly, like numbers. A tabular presentation of data allows for independent number crunching.
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