Slides by. John Loucks. St. Edward s University. Slide South-Western, a part of Cengage Learning

Transcription

1 Slides by John Loucks St. Edward s University Slide 1

2 Chapter 2, Part B Descriptive Statistics: Tabular and Graphical Presentations Exploratory Data Analysis: Stem-and-Leaf Display Crosstabulations and Scatter Diagrams Slide 2

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. Slide 3

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. Slide 4

5 Example: Hudson Auto Repair The manager of Hudson Auto would like to gain 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. Slide 5

6 Stem-and-Leaf Display Example: Hudson Auto Repair Sample of Parts Cost ($) for 50 Tune-ups Slide 6

7 Stem-and-Leaf Display Example: Hudson Auto Repair a stem a leaf Slide 7

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. Slide 8

9 Stretched Stem-and-Leaf Display Example: Hudson Auto Repair Slide 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. The leaf unit indicates how to multiply the stemand-leaf numbers in order to approximate the original data. Slide 10

11 Example: Leaf Unit = 0.1 If we have data with values such as a stem-and-leaf display of these data will be Leaf Unit = Slide 11

12 Example: Leaf Unit = 10 If we have data with values such as a stem-and-leaf display of these data will be Leaf Unit = The 82 in 1682 is rounded down to 80 and is represented as an 8. Slide 12

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. Slide 13

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. Slide 14

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 categorical variable Price Home Style Range Colonial Log Split A-Frame Total < $200,000 > $200, Total Slide 15

16 Crosstabulation Example: Finger Lakes Homes Insights Gained from Preceding Crosstabulation The greatest number of homes (19) in the sample are a split-level style and priced at less than $200,000. Only three homes in the sample are an A-Frame style and priced at $200,000 or more. Slide 16

17 Crosstabulation Example: Finger Lakes Homes Frequency distribution for the price range variable Price Home Style Range Colonial Log Split A-Frame Total < $200,000 > $200, Total Frequency distribution for the home style variable Slide 17

18 Using Excel s PivotTable Report to Create a Crosstabulation Excel Worksheet (showing partial data) A B C D E 1 Home Price ($) Style 2 1 >200K Colonial 3 2 <200K Log 4 3 >200K Log 5 4 <200K A-Frame 6 5 <200K Colonial 7 6 <200K Split-Level 8 7 >200K A-Frame 9 8 >200K Colonial Note: Rows are not shown. Slide 18

19 Using Excel s PivotTable Report to Create a Crosstabulation Displaying the Initial PivotTable Field List and PivotTable Report Step 1 Click the Insert tab on the Ribbon Step 2 In the Tables group, click the icon above the word PivotTable Step 3 When the Create PivotTable dialog box appears: Choose Select a Table or Range Enter A1:C101 in the Table/Range box Choose New Worksheet as the location for the PivotTable Report Click OK Slide 19

20 Using Excel s PivotTable Report to Create a Crosstabulation Setting Up the PivotTable Field List Step 1 In the PivotTable Field List, go to Choose Fields to add to report Drag the Price ($) field to Row Labels area Drag the Style field to Column Labels area Drag the Home field to the Values area Step 2 Click on Sum of Home in the Values area Step 3 Click Value Field Settings from the list of options Step 4 When the Value Field Settings dialog box appears: Under Summarize value field by, choose Count Click OK Slide 20

21 Using Excel s PivotTable Report to Create a Crosstabulation Value Worksheet A B C D E F G 1 Count of Home Style 2 Price ($) Colonial Log Split-Level A-Frame Grand Total 3 <200K >200K Grand Total Slide 21

22 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. Slide 22

23 Crosstabulation: Row Percentages Example: Finger Lakes Homes Price Home Style Range Colonial Log Split A-Frame Total < $200,000 > $200, Note: row totals are actually due to rounding. (Colonial and > $200K)/(All > $200K) x 100 = (12/45) x 100 Slide 23

24 Crosstabulation: Column Percentages Example: Finger Lakes Homes Price Home Style Range Colonial Log Split A-Frame < $200,000 > $200,000 Total (Colonial and > $200K)/(All Colonial) x 100 = (12/30) x 100 Slide 24

25 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. Slide 25

26 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 provides an approximation of the relationship. Slide 26

27 Scatter Diagram A Positive Relationship y x Slide 27

28 Scatter Diagram A Negative Relationship y x Slide 28

29 Scatter Diagram No Apparent Relationship y x Slide 29

30 Scatter Diagram Example: Panthers Football Team 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 Slide 30

31 Number of Points Scored Scatter Diagram y Number of Interceptions x Slide 31

32 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. Slide 32

33 Using Excel s Chart Wizard to Construct a Scatter Diagram and Trendline Excel Worksheet (showing data) A B C Number of Number of 1 Interceptions Points Scored Slide 33

34 Using Excel s Chart Tools to Construct a Scatter Diagram and Trendline Step 1 Select cells A2:B6 Step 2 Click the Insert tab on the Excel Ribbon Step 3 In the Charts group, click Scatter Step 4 When the list of scatter diagram subtypes appears: Click Scatter with only Markers Step 5 In the Chart Layout group, click Layout 1 Step 6 Select the Chart Title and replace it with Scatter Diagram for the Panthers Step 7 Select the Horizontal Axis (Value) Title and replace it with Number of Interceptions... continue Slide 34

35 Using Excel s Chart Tools to Construct a Scatter Diagram and Trendline Step 8 Select the Vertical (Value) Axis Title and replace it with Number of Points Scored Step 9 Right click Series 1 Legend Entry and click Delete To Add a Trendline Step 10 Position the pointer over any data point in the scatter diagram and right-click to display options Step 11 Choose Add Trendline Step 12 When the Format Trendline dialog box appears: Select Trendline Options Choose Linear from Trend/Regression Type list Click Close Slide 35

36 Using Excel s Chart Tools to Construct a Scatter Diagram and Trendline Number of Points Scored A B C Scatter Diagram for the Panthers Num ber of Interceptions Slide 36

37 Tabular and Graphical Methods Categorical Data Data Quantitative Data Tabular Methods Graphical Methods Tabular Methods Graphical Methods Frequency Distribution Rel. Freq. Dist. Percent Freq. Distribution Crosstabulation Bar Graph Pie Chart Frequency Distribution Rel. Freq. Dist. % Freq. Dist. Cum. Freq. Dist. Cum. Rel. Freq. Distribution Cum. % Freq. Distribution Crosstabulation Dot Plot Histogram Ogive Stem-and- Leaf Display Scatter Diagram Slide 37

38 End of Chapter 2, Part B Slide 38