Chapter 3 Graphical Displays of Data

1. DoingStatistics for BusinessData, Inference, and Decision MakingMarilyn K. PelosiTheresa M. Sandifer Chapter 3 Graphical Displays of Data

2. DoingStatistics for Business Chapter 3 Objectives • Graphical Methods for Qualitative Data: Frequency Tables Bar Charts Pie Charts • Graphical Methods for Quantitative Data: Frequency tables Histograms

3. DoingStatistics for Business Chapter 3 Objectives (con’t) • Other Graphical Methods: Dotplots Pareto Diagrams

4. Doing Statistics for Business A Frequency Table or Frequency Distribution is a table containing each category, value or class of values that a variable might have and the number of times that each one occurs in the data. The frequency of the ith class is denoted f.

5. Doing Statistics for Business Figure 3.1 A Frequency Table

6. DoingStatistics for Business The Relative Frequency of a classification is the number of times an observation falls into that classification represented as a portion of the total number of observations. It can be expressed as a fraction, decimal, or percentage.

7. DoingStatistics for Business TRY IT NOW! Student Grades Creating a Frequency Table A professor in an Introductory Statistics course knows that while students dread taking the course, they also have unusually high expectations for their performance. She surveys (anonymously, of course) her students and asks them what grade they expect to get in the course.

8. DoingStatistics for Business TRY IT NOW! Student Grades Creating a Frequency Table (con’t) The raw data are: A C B A A B B B A B A A C B B A F C B D C B B D B A B A Make a frequency table for the data. Include both frequencies and relative frequencies.

9. DoingStatistics for Business The Cumulative Relative Frequency of a class is the sum of the relative frequencies of all classes at or below that class represented as a portion of the total number of observations. It can be expressed as a fraction, decimal, or percentage.

10. DoingStatistics for Business TRY IT NOW! New Product Survey Cumulative Relative Frequencies A marketing research firm conducted a survey of consumers who invariably use a particular brand of of bath soap. The consumers were given a competitor’s version of the same product with non-allergenic enhancements and asked whether they would consider buying the new product. Their answers were given on a scale of 1 to 5 where 1 = would not ever buy this product and 5 = will buy this product immediately.

11. DoingStatistics for Business TRY IT NOW! New Product Survey Cumulative Relative Frequencies (con’t) The raw data from the survey are given below: 5 4 1 4 2 2 3 1 4 4 2 4 3 1 3 3 5 4 4 4 2 3 2 5 4 3 4 4 1 5 Create a frequency table for the data that includes both frequency and cumulative relative frequency.

12. DoingStatistics for Business TRY IT NOW! New Product Survey Cumulative Relative Frequencies (con’t) Which ratings indicate a negative attitude toward the new product? What percentage of people surveyed had a negative attitude? Which rating indicates a neutral attitude? What percentage of the people surveyed had a neutral attitude? Which ratings indicate a positive attitude? What percentage had a positive attitude?

13. DoingStatistics for Business Figure 3.2 Number of Classes & Class Interval for Continuous Data

14. DoingStatistics for Business Figure 3.3Microsoft Excel Frequency Table In Excel, the number in the Bin column is the highest number that is included in the interval, so the first bin is all numbers less than and including 29.50, and the last bin is all numbers greater than 81.58.

15. DoingStatistics for Business TRY IT NOW! Assignment Times Creating a Frequency Table for Continuous Data The instructor for an introductory statistics class wonders about the complaints that she is hearing about the time it takes to complete a computer assignment. The assignments are designed to be done in about 25 minutes. She asks the members of the class to time how long it takes to do the next assignment and to hand the data in with the assignment.

16. DoingStatistics for Business TRY IT NOW! Assignment Times Creating a Frequency Table for Continuous Data (con’t) The data, in minutes, she obtains are: 24.8 27.0 27.9 30.4 33.4 24.8 27.2 27.9 31.1 33.9 24.8 27.4 28.2 31.4 35.3 26.0 27.4 29.4 32.4 35.7 26.0 27.4 29.6 33.1 36.3 26.1 27.6 29.8 33.2 40.4

17. DoingStatistics for Business TRY IT NOW! Assignment Times Creating a Frequency Table for Continuous Data (con’t) Approximately how many classes should the frequency table have? What should the class width be? Create a frequency table for the data.

18. Doing Statistics for Business A Bar Chart represents the frequency or relative frequency from the table in the form of a rectangle or bar.

19. DoingStatistics for Business TRY IT NOW! Student Grades Creating a Bar Chart The instructor who surveyed her students about expected grades wants to create a bar chart from the data. The frequency table for data is

20. DoingStatistics for Business TRY IT NOW! Student Grades Creating a Bar Chart (con’t) Create a bar chart for the data using relative frequency on the y axis. Be sure to label the axes and include an appropriate title.

21. DoingStatistics for Business A Pareto Diagram is a bar chart in which the categories are plotted in order of decreasing relative frequency. In addition to the bars, the cumulative relative frequency of the categories is plotted on the same graph.

22. DoingStatistics for Business A Pie Chart represents data in the form of slices or sections of a circle. Each slice represents a category and the size of the slice is proportional to the relative frequency of the category.

23. DoingStatistics for Business TRY IT NOW! New Product Survey Cumulative Relative Frequencies The marketing research firm that is conducting a survey about customer attitudes toward a new brand of soap would like to look at its data graphically. The frequency table for the data is shown on the following slide:

24. DoingStatistics for Business TRY IT NOW! New Product Survey Cumulative Relative Frequencies (con’t) Create a relative frequency histogram for the data.

25. DoingStatistics for Business In a Dot Plot, each observation is plotted as a point on a single, horizontal axis. The axis is scaled so that each of the data points can be located uniquely on the axis. When there is more than one observation with the same value the points are “stacked” on top of each other.

26. DoingStatistics for Business The Shape of a set of data describes how the data are spread out around the center with respect to the symmetry or skewness of the data.

27. DoingStatistics for Business The Variability of a set of data describes how the data are spread out around the center with respect to the smoothness and magnitude of the variation.

28. DoingStatistics for Business When data are evenly spread out on both sides of the center, we describe the distribution of the data as symmetric.

29. When data are not evenly spread out on either side of the center then we refer to the distribution as being skewed. DoingStatistics for Business

30. DoingStatistics for Business TRY IT NOW! Assignment Times Creating a Frequency Table for Continuous Data The instructor for the introductory statistics class wants to see the data she has collected on the amount of time it took the students to do the assignment graphically.

31. DoingStatistics for Business TRY IT NOW! Assignment Times Creating a Frequency Table for Continuous Data (con’t) The frequency distribution for the data is:

32. DoingStatistics for Business TRY IT NOW! Assignment Times Creating a Frequency Table for Continuous Data (con’t) Create a relative histogram for the data. Use the histogram to describe the distribution of the times the students took to complete the assignment.

33. Doing Statistics for Business Discovery Exercise 3.1 Thinking About Variability A manufacturer of compact disc uses two different suppliers for the jewel boxes used to hold the discs. There have been problems with these boxes in the past. The inside width of the jewel box has critical specifications of 119.0 0.2 mm. If the case is too narrow the disc will not fit in it and if it is too wide, the front label insert slips around. Because it is time to renew the purchasing contracts for the jewel boxes, the CD manufacturer decides to take a look at a sample of the boxes from each supplier.

34. Doing Statistics for Business Discovery Exercise 3.1 Thinking About Variability The data (in mm) for each source is: Make a relative frequency histogram of the data for each supplier

35. Doing Statistics for Business Discovery Exercise 3.1 Thinking About Variability Describe the distribution of jewel box widths for each supplier and compare them. Your company has decided to single source their supply of jewel boxes. The purchasing agent in charge of the accounts argues that supplier B should not get a renewed contract since he observes that the jewel boxes from that source are not centered at the target specification of 119.0 mm while the jewel boxes from supplier A are right on target.

36. Doing Statistics for Business Discovery Exercise 3.1 Thinking About Variability Can you explain to him why, although his observation is true, his decision to use Supplier B is not necessarily correct? What factor has he failed to consider? Which supplier would you recommend they use? Write a short memo to the manager with your recommendation and your supporting reasons.

37. Doing Statistics for Business The basics of creating a chart in Excel, using the Chart Wizard. 1.Highlight the data (Frequency table) that you want to graph. 2. Invoke the Chart Wizard by clicking on the icon on the toolbar. 3. Follow the directions and hints from the Chart Wizard. 4. Edit the graph to include any other features or changes you want.

38. Doing Statistics for Business Figure 3.15Finished Excel Column Chart

39. Doing Statistics for Business Figure 3.16Formatting the Pie Chart

40. Doing Statistics for Business Figure 3.19Pareto Diagram in Excel

41. Doing Statistics for Business The basics of creating a Frequency Table in Excel. 1.Highlight the data for which you want to create the frequency table. 2. Invoke the Pivot Tablet Wizard in Excel by using the Data > Pivot Table Report Menu. 3. Follow the directions that the Pivot Table Wizard gives you. 4. Copy or Edit the pivot table to include any changes you want.

42. Doing Statistics for Business Figure 3.23Finished Pivot Table

43. Doing Statistics for Business The basics of creating Histograms in Excel. 1.From the Data Analysis dialog box, select Histogram and click OK. The Histogram dialog box will open. 2. Position the cursor in the Input Range text box and highlight the range that contains the data, B1:B208. 3. Click the checkbox for Labels since the range contains the variable name. 4. Excel calls the class intervals for continuous data Bins. Leave the Bin text box empty this time and let Excel pick the class intervals.

44. Doing Statistics for Business The basics of creating Histograms in Excel. (con’t) 5. Click the radio button for Output Range, position the cursor in the text box, and click on the cell where you want the top left corner of the output to appear. 6. Finally, click the checkbox for Chart Output. The completed dialog box appears in Figure 3.25 (Slide 43). 7. Click OK and the output will appear as shown in Figure 3.26 (Slide 44).

45. Doing Statistics for Business Figure 3.25Completed Histogram Dialog Box

46. Doing Statistics for Business Figure 3.26Output from Histogram Tool

47. Doing Statistics for Business Figure 3.31Completed Histogram

48. Doing Statistics for Business Chapter 3 Summary In this chapter you have learned: • The purpose of descriptive statistics is to turn data into information. • Qualitative data can be displayed using bar charts or pie charts. • Quantitative data are usually displayed using a histogram or dotplot.

49. Doing Statistics for Business Chapter 3 Summary (con’t) • Graphical displays of data can be used to describe data in terms of center, shape, and variability. • Computer software packages, such as Excel, greatly enhance the quality of the finished graphs.