1 / 47

Slides by JOHN LOUCKS St. Edward’s University

Slides by JOHN LOUCKS St. Edward’s University. y. x. Chapter 2 Descriptive Statistics: Tabular and Graphical Presentations Part B. Exploratory Data Analysis Crosstabulations and Scatter Diagrams. Exploratory Data Analysis.

sheadon
Download Presentation

Slides by JOHN LOUCKS St. Edward’s University

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Slides by JOHN LOUCKS St. Edward’s University

  2. y x Chapter 2Descriptive Statistics:Tabular and Graphical PresentationsPart B • Exploratory Data Analysis • Crosstabulations and Scatter Diagrams

  3. Exploratory Data Analysis • The techniques of exploratory data analysis consist of • simple arithmetic and easy-to-draw pictures that can • be used to summarize data quickly. • One such technique is the stem-and-leaf display.

  4. Stem-and-Leaf Display • A stem-and-leaf display shows both the rank order • and shape of the distribution of the data. • It is similar to a histogram on its side, but it has the • advantage of showing the actual data values. • The first digits of each data item are arranged to the • left of a vertical line. • To the right of the vertical line we record the last • digit for each item in rank order. • Each line in the display is referred to as a stem. • Each digit on a stem is a leaf.

  5. Example: Hudson Auto Repair The manager of Hudson Auto would like to have a better understanding of the cost of parts used in the engine tune-ups performed in the shop. She examines 50 customer invoices for tune-ups. The costs of parts, rounded to the nearest dollar, are listed on the next slide.

  6. Example: Hudson Auto Repair • Sample of Parts Cost ($) for 50 Tune-ups

  7. Stem-and-Leaf Display 5 6 7 8 9 10 2 7 2 2 2 2 5 6 7 8 8 8 9 9 9 1 1 2 2 3 4 4 5 5 5 6 7 8 9 9 9 0 0 2 3 5 8 9 1 3 7 7 7 8 9 1 4 5 5 9 a stem a leaf

  8. Stretched Stem-and-Leaf Display • If we believe the original stem-and-leaf display has • condensed the data too much, we can stretch the • display by using two stems for each leading digit(s). • Whenever a stem value is stated twice, the first value • corresponds to leaf values of 0 - 4, and the second • value corresponds to leaf values of 5 - 9.

  9. Stretched Stem-and-Leaf Display 5 5 6 6 7 7 8 8 9 9 10 10 2 7 2 2 2 2 5 6 7 8 8 8 9 9 9 1 1 2 2 3 4 4 5 5 5 6 7 8 9 9 9 0 0 2 3 5 8 9 1 3 7 7 7 8 9 1 4 5 5 9

  10. Stem-and-Leaf Display • Leaf Units • A single digit is used to define each leaf. • In the preceding example, the leaf unit was 1. • Leaf units may be 100, 10, 1, 0.1, and so on. • Where the leaf unit is not shown, it is assumed • to equal 1.

  11. Example: Leaf Unit = 0.1 If we have data with values such as 8.6 11.7 9.4 9.1 10.2 11.0 8.8 a stem-and-leaf display of these data will be Leaf Unit = 0.1 8 9 10 11 6 8 1 4 2 0 7

  12. Example: Leaf Unit = 10 If we have data with values such as 1806 1717 1974 1791 1682 1910 1838 a stem-and-leaf display of these data will be Leaf Unit = 10 16 17 18 19 8 The 82 in 1682 is rounded down to 80 and is represented as an 8. 1 9 0 3 1 7

  13. Crosstabulations and Scatter Diagrams • Thus far we have focused on methods that are used • to summarize the data for one variable at a time. • Often a manager is interested in tabular and • graphical methods that will help understand the • relationship between two variables. • Crosstabulation and a scatter diagram are two • methods for summarizing the data for two variables • simultaneously.

  14. Crosstabulation • A crosstabulation is a tabular summary of data for two variables. • Crosstabulation can be used when: • one variable is qualitative and the other is • quantitative, • both variables are qualitative, or • both variables are quantitative. • The left and top margin labels define the classes for • the two variables.

  15. Crosstabulation • Example: Finger Lakes Homes The number of Finger Lakes homes sold for each style and price for the past two years is shown below. quantitative variable qualitative variable Home Style Price Range Colonial Log Split A-Frame Total 18 6 19 12 55 45 < $99,000 > $99,000 12 14 16 3 30 20 35 15 Total 100

  16. Crosstabulation • Insights Gained from Preceding Crosstabulation • The greatest number of homes (19) in the sample • are a split-level style and priced at less than or • equal to $99,000. • Only three homes in the sample are an A-Frame • style and priced at more than $99,000.

  17. Crosstabulation Frequency distribution for the price variable Home Style Price Range Colonial Log Split A-Frame Total 18 6 19 12 55 45 < $99,000 > $99,000 12 14 16 3 30 20 35 15 Total 100 Frequency distribution for the home style variable

  18. Using Excel’s PivotTable Reportto Construct a Crosstabulation • Excel Worksheet (showing partial data) Note: Rows 10-101 are not shown.

  19. . . . continue Using Excel’s PivotTable Reportto Construct a Crosstabulation • Using the PivotTable Report Step 1 Select the Data menu Step 2 Choose the PivotTable and PivotChart Report Step 3 When the PivotTable and PivotChart Wizard – Step 1 of 3 dialog box appears: Choose Microsoft Excel list or database Choose PivotTable Click Next >

  20. . . . continue Using Excel’s PivotTable Reportto Construct a Crosstabulation • Using the PivotTable Report Step 4 When the PivotTable and PivotChart Wizard – Step 2 of 3 dialog box appears: Enter A1:C101 in the Range box Click Next >

  21. . . . continue Using Excel’s PivotTable Reportto Construct a Crosstabulation • Using the PivotTable Report Step 5 When the PivotTable and PivotChart Wizard – Step 3 of 3 dialog box appears: Select New Worksheet Click Layout

  22. . . . continue Using Excel’s PivotTable Reportto Construct a Crosstabulation Step 5(continued) When the PivotTable and PivotChart Wizard – Layout diagram appears: • Using the PivotTable Report Drag the Price ($) field button to the ROW section of the diagram Drag the Style field button to the COLUMN section of the diagram Drag the Home field button to the DATA section of the diagram Double click the Count of Home field button in the data section

  23. Using Excel’s PivotTable Reportto Construct a Crosstabulation • Using the PivotTable Report Step 5(continued) When the PivotTable Field dialog box appears: Choose Count under Summarized by: Click OK Click OK When the PivotTable and PivotChart Wizard Step 3 of 3 dialog box reappears: Click Finish >

  24. Using Excel’s PivotTable Reportto Construct a Crosstabulation

  25. Using Excel’s PivotTable Reportto Construct a Crosstabulation

  26. Using Excel’s PivotTable Reportto Construct a Crosstabulation • Value Worksheet Note: Columns A-C are not shown.

  27. Crosstabulation: Row or Column Percentages • Converting the entries in the table into row percentages or column percentages can provide additional insight about the relationship between the two variables.

  28. Crosstabulation: Row Percentages Home Style Price Range Colonial Log Split A-Frame Total 32.73 10.91 34.55 21.82 100 100 < $99,000 > $99,000 26.67 31.11 35.56 6.67 Note: row totals are actually 100.01 due to rounding. (Colonial and > $99K)/(All >$99K) x 100 = (12/45) x 100

  29. Crosstabulation: Column Percentages Home Style Price Range Colonial Log Split A-Frame 60.00 30.00 54.29 80.00 < $99,000 > $99,000 40.00 70.00 45.71 20.00 100 100 100 100 Total (Colonial and > $99K)/(All Colonial) x 100 = (12/30) x 100

  30. Crosstabulation: Simpson’s Paradox • Data in two or more crosstabulations are often aggregated to produce a summary crosstabulation. • We must be careful in drawing conclusions about the • relationship between the two variables in the • aggregated crosstabulation. • Simpson’ Paradox: In some cases the conclusions based upon an aggregated crosstabulation can be completely reversed if we look at the unaggregated data. suggests the overall relationship between the variables.

  31. Scatter Diagram and Trendline • A scatter diagram is a graphical presentation of the • relationship between two quantitative variables. • One variable is shown on the horizontal axis and the • other variable is shown on the vertical axis. • The general pattern of the plotted points suggests the • overall relationship between the variables. • A trendline is an approximation of the relationship.

  32. Scatter Diagram • A Positive Relationship y x

  33. Scatter Diagram • A Negative Relationship y x

  34. Scatter Diagram • No Apparent Relationship y x

  35. Example: Panthers Football Team • Scatter Diagram The Panthers football team is interested in investigating the relationship, if any, between interceptions made and points scored. x = Number of Interceptions y = Number of Points Scored 14 24 18 17 30 1 3 2 1 3

  36. 35 30 25 20 15 10 5 0 1 0 2 3 4 Scatter Diagram y Number of Points Scored x Number of Interceptions

  37. Example: Panthers Football Team • Insights Gained from the Preceding Scatter Diagram • The scatter diagram indicates a positive relationship • between the number of interceptions and the • number of points scored. • Higher points scored are associated with a higher • number of interceptions. • The relationship is not perfect; all plotted points in • the scatter diagram are not on a straight line.

  38. Using Excel’s Chart Wizard to Constructa Scatter Diagram and Trendline • Excel Worksheet (showing data)

  39. . . . continue Using Excel’s Chart Wizardto Construct a Scatter Diagram Step 1 Select cells A1:B6 Step 2 Click the Chart Wizard button on standard toolbar Step 3 When the Chart Wizard - Step 1 of 4 - Chart Type dialog box appears: Choose XY (Scatter) in the Chart Type list Choose Scatter from the Chart subtype display Click Next >

  40. . . . continue Using Excel’s Chart Wizardto Construct a Scatter Diagram Step 4 When the Chart Wizard- Step 2 of 4 -Chart Source Data dialog box appears: Click Next >

  41. . . . continue Using Excel’s Chart Wizardto Construct a Scatter Diagram Step 5 When the Chart Wizard - Step 3 of 4 – Chart Options dialog box appears: Select the Titles tab and then Type Scatter Diagram for the Panthers in the Chart title: box Type Number of Interceptions in the Value (X) axis: box Type Number of Points Scored in the Value (Y) axis: box

  42. Using Excel’s Chart Wizardto Construct a Scatter Diagram Step 5(continued) Select the Legend tab and then Remove the check in the Show Legend box Click Next > Step 6 When the Chart Wizard – Step 4 of 4 - Chart Location dialog box appears: Specify a location for the new chart Click Finish

  43. Using Excel’s Chart Wizard to Construct a Scatter Diagram

  44. Using Excel’s Chart Wizard to Constructa Scatter Diagram and Trendline • Adding a Trendline Step 1 Position the mouse pointer over any data point in the scatter diagram and right click Step 2 Choose Add Trendline Step 3 When the Add Trendline dialog box appears: Select the Type tab and then Choose Linear from the Trend/ Regression type display Click OK

  45. Using Excel’s Chart Wizard to Constructa Scatter Diagram and Trendline

  46. Tabular and Graphical Procedures Data Qualitative Data Quantitative Data Tabular Methods Graphical Methods Tabular Methods Graphical Methods • Bar Graph • Pie Chart • Frequency • Distribution • Rel. Freq. Dist. • Percent Freq. • Distribution • Crosstabulation • Histogram • Ogive • Scatter • Diagram • Frequency • Distribution • Rel. Freq. Dist. • Cum. Freq. Dist. • Cum. Rel. Freq. • Distribution • Stem-and-Leaf • Display • Crosstabulation

  47. End of Chapter 2, Part B

More Related