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

2. 2 2 Slide Chapter 2, Part A Descriptive Statistics: Tabular and Graphical Presentations n Summarizing Categorical Data n Summarizing Quantitative Data

3. 3 3 Slide Summarizing Categorical Data n Frequency Distribution n Relative Frequency Distribution n Percent Frequency Distribution n Bar Chart n Pie Chart n Crosstabulation

4. 4 4 Slide A frequency distribution is a tabular summary of A frequency distribution is a tabular summary of data showing the frequency (or number) of items data showing the frequency (or number) of items in each of several non-overlapping classes. in each of several non-overlapping classes. A frequency distribution is a tabular summary of A frequency distribution is a tabular summary of data showing the frequency (or number) of items data showing the frequency (or number) of items in each of several non-overlapping classes. in each of several non-overlapping classes. The objective is to provide insights about the data The objective is to provide insights about the data that cannot be quickly obtained by looking only at that cannot be quickly obtained by looking only at the original data. the original data. The objective is to provide insights about the data The objective is to provide insights about the data that cannot be quickly obtained by looking only at that cannot be quickly obtained by looking only at the original data. the original data. Frequency Distribution

5. 5 5 Slide Guests staying at Marada Inn were asked to rate the quality of their accommodations as being excellent, above average, average, below average, or poor. The ratings provided by a sample of 20 guests are: Below Average Below Average Above Average Above Average Average Average Above Average Above Average Average Average Above Average Above Average Average Average Above Average Above Average Below Average Below Average Poor Poor Excellent Excellent Above Average Above Average Average Average Above Average Above Average Below Average Below Average Poor Poor Above Average Above Average Average Average Frequency Distribution n Example: Marada Inn

6. 6 6 Slide Frequency Distribution Poor Below Average Average Above Average Excellent 2 3 5 9 1 Total 20 RatingFrequency n Example: Marada Inn

7. 7 7 Slide Using Excel’s COUNTIF Function to Construct a Frequency Distribution n Excel Formula Worksheet Note: Rows 9-21 are not shown.

8. 8 8 Slide n Excel Value Worksheet Using Excel’s COUNTIF Function to Construct a Frequency Distribution Note: Rows 9-21 are not shown.

9. 9 9 Slide The relative frequency of a class is the fraction or The relative frequency of a class is the fraction or proportion of the total number of data items proportion of the total number of data items belonging to the class. belonging to the class. The relative frequency of a class is the fraction or The relative frequency of a class is the fraction or proportion of the total number of data items proportion of the total number of data items belonging to the class. belonging to the class. A relative frequency distribution is a tabular A relative frequency distribution is a tabular summary of a set of data showing the relative summary of a set of data showing the relative frequency for each class. frequency for each class. A relative frequency distribution is a tabular A relative frequency distribution is a tabular summary of a set of data showing the relative summary of a set of data showing the relative frequency for each class. frequency for each class. Relative Frequency Distribution

10. 10 Slide Percent Frequency Distribution The percent frequency of a class is the relative The percent frequency of a class is the relative frequency multiplied by 100. frequency multiplied by 100. The percent frequency of a class is the relative The percent frequency of a class is the relative frequency multiplied by 100. frequency multiplied by 100. A percent frequency distribution is a tabular A percent frequency distribution is a tabular summary of a set of data showing the percent summary of a set of data showing the percent frequency for each class. frequency for each class. A percent frequency distribution is a tabular A percent frequency distribution is a tabular summary of a set of data showing the percent summary of a set of data showing the percent frequency for each class. frequency for each class.

11. 11 Slide Relative Frequency and Percent Frequency Distributions Poor Below Average Average Above Average Excellent.10.15.25.45.05 Total 1.00 10 15 25 45 5 100 Relative RelativeFrequency Percent PercentFrequency Rating.10(100) = 10 1/20 =.05 n Example: Marada Inn

12. 12 Slide n Excel Formula Worksheet Note: Columns A-B and rows 9-21 and are not shown. Using Excel to Construct Relative Frequency and Percent Frequency Distributions

13. 13 Slide n Excel Value Worksheet Using Excel to Construct Relative Frequency and Percent Frequency Distributions Note: Columns A-B and rows 9-21 and are not shown.

14. 14 Slide Bar Chart (In Excel this is called a Column Chart) A bar chart is a graphical device for depicting A bar chart is a graphical device for depicting qualitative data. qualitative data. On one axis (usually the horizontal axis), we specify On one axis (usually the horizontal axis), we specify the labels that are used for each of the classes. the labels that are used for each of the classes. A frequency, relative frequency, or percent frequency A frequency, relative frequency, or percent frequency scale can be used for the other axis (usually the scale can be used for the other axis (usually the vertical axis). vertical axis). Using a bar of fixed width drawn above each class Using a bar of fixed width drawn above each class label, we extend the height appropriately. label, we extend the height appropriately. The bars are separated to emphasize the fact that each The bars are separated to emphasize the fact that each class is a separate category. class is a separate category.

15. 15 Slide Poor Below Average Below Average Above Average Above Average Excellent Frequency Rating Bar Chart (In Excel this is called a Column Chart) 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 Marada Inn Quality Ratings

16. 16 Slide Using Excel’s Chart Tools to Construct a Bar Chart Step 1. Select cells C1:D6 Step 2. Click the Insert tab on the Ribbon Step 4. When the list of column chart subtypes appears: Go to the 2-D Column section Go to the 2-D Column section Click Clustered Column (the leftmost chart) Click Clustered Column (the leftmost chart) Step 5. In the Chart Layouts group, click the More button (the downward pointing arrow with a line over it) (the downward pointing arrow with a line over it) to display all the options to display all the options … continued Step 3. In the Charts group, click Column

17. 17 Slide Step 6. Choose Layout 9 Using Excel’s Chart Tools to Construct a Bar Chart … continued Step 7. Click the Chart Title and replace it with Marada Inn Quality Ratings Marada Inn Quality Ratings Step 8. Click the Horizontal Axis (Category) Title and replace it with Quality Rating replace it with Quality Rating Step 9. Click the Vertical Axis (Value) Title and replace it with Frequency replace it with Frequency Step 10. Right click the Series 1 Legend Entry and choose Delete from the list of options that appear Delete from the list of options that appear

18. 18 Slide Step 11. Right click the vertical axis and choose Format Axis from the options that appear Format Axis from the options that appear Using Excel’s Chart Tools to Construct a Bar Chart Step 12. When the Format Axis dialog box appears: Go to the Axis Options section Go to the Axis Options section Select Fixed for Major Unit and enter 2.0 in Select Fixed for Major Unit and enter 2.0 in the corresponding box the corresponding box Click Close Click Close

19. 19 Slide Using Excel’s Chart Tools to Construct a Bar Chart

20. 20 Slide Pie Chart The pie chart is a commonly used graphical device The pie chart is a commonly used graphical device for presenting relative frequency distributions for for presenting relative frequency distributions for qualitative data. qualitative data. n First draw a circle; then use the relative frequencies to subdivide the circle into sectors that correspond to to subdivide the circle into sectors that correspond to the relative frequency for each class. the relative frequency for each class. n Since there are 360 degrees in a circle, a class with a relative frequency of.25 would consume.25(360) = 90 relative frequency of.25 would consume.25(360) = 90 degrees of the circle. degrees of the circle.

21. 21 Slide Below Average 15% Below Average 15% Average 25% Average 25% Above Average 45% Above Average 45% Poor 10% Poor 10% Excellent 5% Excellent 5% Marada InnQuality Ratings Marada Inn Quality Ratings Pie Chart

22. 22 Slide n Insights Gained from the Preceding Pie Chart Example: Marada Inn One-half of the customers surveyed gave Marada One-half of the customers surveyed gave Marada a quality rating of “above average” or “excellent” a quality rating of “above average” or “excellent” (looking at the left side of the pie). This might (looking at the left side of the pie). This might please the manager. please the manager. For each customer who gave an “excellent” rating, For each customer who gave an “excellent” rating, there were two customers who gave a “poor” there were two customers who gave a “poor” rating (looking at the top of the pie). This should rating (looking at the top of the pie). This should displease the manager. displease the manager.

23. 23 Slide Excel’s chart tools can be used to develop a pie chart for the Marada quality rating data in much the same way we developed the bar chart. Using Excel’s Chart Tools to Construct a Pie Chart The major difference is that in step 3 we would choose Pie in the Charts group.

24. 24 Slide Using Excel’s Chart Tools to Construct a Pie Chart

25. 25 Slide Excel’s PivotTable Report and PivotChart Report You have now seen how Excel’s COUNTIF function can be used to develop a frequency distribution and Excel’s Chart Tools can be used to create bar and pie charts. But there is a more powerful set of Excel tools that can be used for categorical data: PivotTable report PivotTable report PivotChart report PivotChart report

26. 26 Slide Summarizing Quantitative Data n Frequency Distribution n Relative Frequency and Percent Frequency Distributions Percent Frequency Distributions n Dot Plot n Histogram n Cumulative Distributions n Ogive n Stem-Leaf Display n Crosstabulation n Scatter Diagram

27. 27 Slide 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. n Example: Hudson Auto Repair Frequency Distribution

28. 28 Slide Sample of Parts Cost($) for 50 Tune-ups Frequency Distribution n Example: Hudson Auto Repair

29. 29 Slide Frequency Distribution n Guidelines for Selecting Number of Classes Use between 5 and 20 classes. Use between 5 and 20 classes. Data sets with a larger number of elements Data sets with a larger number of elements usually require a larger number of classes. usually require a larger number of classes. Smaller data sets usually require fewer classes. Smaller data sets usually require fewer classes.

30. 30 Slide Frequency Distribution n Guidelines for Selecting Width of Classes Use classes of equal width. Use classes of equal width. Approximate Class Width = Approximate Class Width =

31. 31 Slide Frequency Distribution If we choose six classes: 50-59 60-69 70-79 80-89 90-99 100-109 2 13 16 7 7 5 Total 50 Parts Cost ($) Frequency Approximate Class Width = (109 - 52)/6 = 9.5  10 n Example: Hudson Auto Repair

32. 32 Slide Using Excel’s PivotTable Report to Construct a Frequency Distribution Step 1 Click the Insert tab on the Ribbon Step 2 In the Tables group, click the icon above the word PivotTable word PivotTable Step 3 When the Create PivotTable dialog box appears: Choose Select a table or range Choose Select a table or range Enter A1:A51 in the Table/Range box Enter A1:A51 in the Table/Range box Choose Existing Worksheet as the location Choose Existing Worksheet as the location for the PivotTable for the PivotTable Enter C1 in the Location box Enter C1 in the Location box Click OK Click OK … continued

33. 33 Slide Step 5 Click on Sum of Parts Cost in the Values area Step 6 Click Value Field Settings from the list of options that appear that appear Step 7 When the Value Field Settings dialog box appears: Under Summarize value field by, choose Count Under Summarize value field by, choose Count Click OK Click OK Step 4 In the PivotTable Field List, go to Choose Fields to add to report: to add to report: Drag the Parts Cost field to the Row Labels area Drag the Parts Cost field to the Row Labels area Drag the Parts Cost field to the Values area Drag the Parts Cost field to the Values area Using Excel’s PivotTable Report to Construct a Frequency Distribution

34. 34 Slide Step 2 Choose Group from the list of options that appears Step 3 When the Grouping dialog box appears: Enter 50 in the Starting at box Enter 50 in the Starting at box Enter 109 in the Ending at box Enter 109 in the Ending at box Enter 10 in the By box Enter 10 in the By box Click OK Click OK Step 1 Right click any cell in the PivotTable report containing a parts cost. containing a parts cost. Using Excel’s PivotTable Report to Construct a Frequency Distribution To construct the frequency distribution, we must group the rows containing parts costs.

35. 35 Slide n Excel Value Worksheet Note: Rows 9-51 are not shown. ABCD 1Parts Cost Count of Parts Cost 29150-592 37160-6913 410470-7916 58580-897 66290-997 778100-1095 869 50 Grand Total Using Excel’s PivotTable Report to Construct a Frequency Distribution

36. 36 Slide Relative Frequency and Percent Frequency Distributions 50-59 50-59 60-69 60-69 70-79 70-79 80-89 80-89 90-99 90-99 100-109 100-109 Parts Cost ($).04.26.32.14.14.10 Total 1.00 Relative RelativeFrequency 4 26 32 14 14 10 100 Percent Frequency Frequency 2/502/50.04(100).04(100) n Example: Hudson Auto Repair

37. 37 Slide Only 4% of the parts costs are in the $50-59 class. Only 4% of the parts costs are in the $50-59 class. The greatest percentage (32% or almost one-third) The greatest percentage (32% or almost one-third) of the parts costs are in the $70-79 class. of the parts costs are in the $70-79 class. 30% of the parts costs are under $70. 30% of the parts costs are under $70. 10% of the parts costs are $100 or more. 10% of the parts costs are $100 or more. Insights Gained from the % Frequency Distribution: Relative Frequency and Percent Frequency Distributions n Example: Hudson Auto Repair

38. 38 Slide Dot Plot n One of the simplest graphical summaries of data is a dot plot. n A horizontal axis shows the range of data values. n Then each data value is represented by a dot placed above the axis.

39. 39 Slide Dot Plot 5060708090100110 50 60 70 80 90 100 110 Cost ($) Tune-up Parts Cost n Example: Hudson Auto Repair

40. 40 Slide Histogram Another common graphical presentation of Another common graphical presentation of quantitative data is a histogram. quantitative data is a histogram. The variable of interest is placed on the horizontal The variable of interest is placed on the horizontal axis. axis. A rectangle is drawn above each class interval with A rectangle is drawn above each class interval with its height corresponding to the interval’s frequency, its height corresponding to the interval’s frequency, relative frequency, or percent frequency. relative frequency, or percent frequency. Unlike a bar graph, a histogram has no natural Unlike a bar graph, a histogram has no natural separation between rectangles of adjacent classes. separation between rectangles of adjacent classes.

41. 41 Slide Histogram 2 2 4 4 6 6 8 8 10 12 14 16 18 Parts Cost ($) Parts Cost ($) Frequency 50  59 60  69 70  79 80  89 90  99 100-110 Tune-up Parts Cost n Example: Hudson Auto Repair

42. 42 Slide Using Excel’s Chart Tools to Construct a Histogram Step 1. Select cells C2:D7 Step 2. Click the Insert tab on the Ribbon Step 4. When the list of column chart subtypes appears: Go to the 2-D Column section Go to the 2-D Column section Click Clustered Column (the leftmost chart) Click Clustered Column (the leftmost chart) … continued Step 3. In the Charts group, click Column Step 5. In the Chart Layouts group, click the More button (the downward pointing arrow with button (the downward pointing arrow with a line over it) to display all the options a line over it) to display all the options

43. 43 Slide Using Excel’s Chart Tools to Construct a Histogram Step 6. Choose Layout 8 Step 7. Select the Chart Title and replace it with Tune-up Parts Cost Tune-up Parts Cost Step 9. Select the Vertical (Value) Axis Title and replace it with Frequency it with Frequency Step 8. Select the Horizontal (Category) Axis Title and replace it with Parts Cost ($) replace it with Parts Cost ($)

44. 44 Slide Using Excel’s Chart Tools to Construct a Histogram

45. 45 Slide n Symmetric Histogram Relative Frequency.05.10.15.20.25.30.35 0 0 Left tail is the mirror image of the right tail Left tail is the mirror image of the right tail Examples: heights and weights of people Examples: heights and weights of people

46. 46 Slide Histogram n Moderately Skewed Left Relative Frequency.05.10.15.20.25.30.35 0 0 A longer tail to the left A longer tail to the left Example: exam scores Example: exam scores

47. 47 Slide n Moderately Right Skewed Histogram Relative Frequency.05.10.15.20.25.30.35 0 0 A Longer tail to the right A Longer tail to the right Example: housing values Example: housing values

48. 48 Slide Histogram n Highly Skewed Right Relative Frequency.05.10.15.20.25.30.35 0 0 A very long tail to the right A very long tail to the right Example: executive salaries Example: executive salaries

49. 49 Slide Cumulative frequency distribution  shows the Cumulative frequency distribution  shows the number of items with values less than or equal to the number of items with values less than or equal to the upper limit of each class.. upper limit of each class.. Cumulative frequency distribution  shows the Cumulative frequency distribution  shows the number of items with values less than or equal to the number of items with values less than or equal to the upper limit of each class.. upper limit of each class.. Cumulative relative frequency distribution – shows Cumulative relative frequency distribution – shows the proportion of items with values less than or the proportion of items with values less than or equal to the upper limit of each class. equal to the upper limit of each class. Cumulative relative frequency distribution – shows Cumulative relative frequency distribution – shows the proportion of items with values less than or the proportion of items with values less than or equal to the upper limit of each class. equal to the upper limit of each class. Cumulative Distributions Cumulative percent frequency distribution – shows Cumulative percent frequency distribution – shows the percentage of items with values less than or the percentage of items with values less than or equal to the upper limit of each class. equal to the upper limit of each class. Cumulative percent frequency distribution – shows Cumulative percent frequency distribution – shows the percentage of items with values less than or the percentage of items with values less than or equal to the upper limit of each class. equal to the upper limit of each class.

50. 50 Slide Cumulative Distributions n Hudson Auto Repair <59 <69 <79 <89 <99 <109 Cost ($) Cumulative CumulativeFrequency RelativeFrequency CumulativePercent Frequency Frequency 2 15 31 38 45 50.04.30.62.76.90 1.00 4 30 62 76 90 100 2 + 13 15/5015/50.30(100).30(100)

51. 51 Slide Ogive n An ogive is a graph of a cumulative distribution. n The data values are shown on the horizontal axis. n Shown on the vertical axis are the: cumulative frequencies, or cumulative frequencies, or cumulative relative frequencies, or cumulative relative frequencies, or cumulative percent frequencies cumulative percent frequencies n The frequency (one of the above) of each class is plotted as a point. n The plotted points are connected by straight lines.

52. 52 Slide Because the class limits for the parts-cost data are 50-59, 60-69, and so on, there appear to be one-unit gaps from 59 to 60, 69 to 70, and so on. Because the class limits for the parts-cost data are 50-59, 60-69, and so on, there appear to be one-unit gaps from 59 to 60, 69 to 70, and so on. Ogive These gaps are eliminated by plotting points halfway between the class limits. These gaps are eliminated by plotting points halfway between the class limits. Thus, 59.5 is used for the 50-59 class, 69.5 is used for the 60-69 class, and so on. Thus, 59.5 is used for the 50-59 class, 69.5 is used for the 60-69 class, and so on. n Hudson Auto Repair

53. 53 Slide Parts Parts Cost ($) Parts Parts Cost ($) 20 40 60 80 100 Cumulative Percent Frequency 50 60 70 80 90 100 110 (89.5, 76) Ogive with Cumulative Percent Frequencies Cumulative Percent Frequencies Tune-up Parts Cost n Example: Hudson Auto Repair

54. 54 Slide Using Excel’s PivotChart Report You have now seen how Excel’s PivotTable report can be used to construct a frequency distribution for quantitative data and how Excel’s Chart tools can be used to construct the corresponding histogram. However, Excel’s PivotChart report can be used to develop a frequency distribution and a graphical display at the same time.

55. 55 Slide Using Excel’s PivotChart Report Step 1. Click the Insert tab on the Ribbon Step 2. In the Tables group, click the word PivotTable Step 4. When the Create PivotTable with PivotChart dialog box appears: dialog box appears: Choose Select a table or range Choose Select a table or range Enter A1:A51 in the Table/Range box Enter A1:A51 in the Table/Range box Choose Existing Worksheet as the location for Choose Existing Worksheet as the location for the PivotTable and PivotChart the PivotTable and PivotChart Enter C1 in the Location box Enter C1 in the Location box Click OK Click OK … continued Step 3. Choose PivotChart from the options that appear

56. 56 Slide Using Excel’s PivotChart Report Step 5. In the PivotTable Field List, go to Choose Fields to add to report to add to report Drag the Parts Cost field to the Axis Fields Drag the Parts Cost field to the Axis Fields (Categories) area (Categories) area Drag the Parts Cost field to the Values area Drag the Parts Cost field to the Values area Step 6. Click Sum of Parts Cost in the Values area Step 7. Click Value Field Settings from the list of options that appear that appear Step 8. When the Value Field Settings dialog appears: Under Summarize value field by, choose Count Under Summarize value field by, choose Count Click OK Click OK … continued

57. 57 Slide Using Excel’s PivotChart Report Step 9. Right click cell C2 n the PivotTable report or any other cell containing a parts cost other cell containing a parts cost Step 10. Choose Group from the list of options Step 11. When the Grouping dialog box appears: Enter ___ in the Starting at box Enter ___ in the Starting at box Enter ___ in the Ending at box Enter ___ in the Ending at box Click OK Click OK Step 12. Click inside the resulting PivotChart Step 13. Click the Design tab on the Ribbon … continued

58. 58 Slide Using Excel’s PivotChart Report Step 14. In the Chart Layouts group, click the More button (the downward pointing arrow with a button (the downward pointing arrow with a line over it) to display all the options line over it) to display all the options Step 15. Choose Layout 8 Step 16. Select the Chart Title and replace it with Tune-up Parts Costs Tune-up Parts Costs Step 17. Select the Horizontal Axis (Category) Title and replace it with Parts Cost ($) replace it with Parts Cost ($) Step 18. Select the Vertical (Value) Axis Title and replace it with Frequency it with Frequency

59. 59 Slide End of Chapter 2, Part A

60. 60 Slide Chapter 2, Part B Descriptive Statistics: Tabular and Graphical Presentations n Crosstabulations and Scatter Diagrams n Exploratory Data Analysis: Stem-and-Leaf Display

61. 61 Slide Exploratory Data Analysis The techniques of exploratory data analysis consist of The techniques of exploratory data analysis consist of simple arithmetic and easy-to-draw pictures that can simple arithmetic and easy-to-draw pictures that can be used to summarize data quickly. be used to summarize data quickly. One such technique is the stem-and-leaf display. One such technique is the stem-and-leaf display.

62. 62 Slide Stem-and-Leaf Display Each digit on a stem is a leaf. Each digit on a stem is a leaf. Each line in the display is referred to as a stem. Each line in the display is referred to as a stem. To the right of the vertical line we record the last To the right of the vertical line we record the last digit for each item in rank order. digit for each item in rank order. The first digits of each data item are arranged to the The first digits of each data item are arranged to the left of a vertical line. left of a vertical line. It is similar to a histogram on its side, but it has the It is similar to a histogram on its side, but it has the advantage of showing the actual data values. advantage of showing the actual data values. A stem-and-leaf display shows both the rank order A stem-and-leaf display shows both the rank order and shape of the distribution of the data. and shape of the distribution of the data.

63. 63 Slide 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.

64. 64 Slide Sample of Parts Cost ($) for 50 Tune-ups Example: Hudson Auto Repair Example: Hudson Auto Repair Stem-and-Leaf Display

65. 65 Slide 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 Example: Hudson Auto Repair Example: Hudson Auto Repair

66. 66 Slide Stretched Stem-and-Leaf Display Whenever a stem value is stated twice, the first value Whenever a stem value is stated twice, the first value corresponds to leaf values of 0  4, and the second corresponds to leaf values of 0  4, and the second value corresponds to leaf values of 5  9. value corresponds to leaf values of 5  9. If we believe the original stem-and-leaf display has If we believe the original stem-and-leaf display has condensed the data too much, we can stretch the condensed the data too much, we can stretch the display by using two stems for each leading digit(s). display by using two stems for each leading digit(s).

67. 67 Slide Stretched Stem-and-Leaf Display 5 5 9 1 4 7 7 7 8 9 1 3 5 8 9 0 0 2 3 5 5 5 6 7 8 9 9 9 1 1 2 2 3 4 4 5 6 7 8 8 8 9 9 9 2 2 2 2 7 2 5 5 6 6 7 7 8 8 9 9 10 10 Example: Hudson Auto Repair Example: Hudson Auto Repair

68. 68 Slide Stem-and-Leaf Display Leaf Units Leaf Units Where the leaf unit is not shown, it is assumed Where the leaf unit is not shown, it is assumed to equal 1. to equal 1. Leaf units may be 100, 10, 1, 0.1, and so on. Leaf units may be 100, 10, 1, 0.1, and so on. In the preceding example, the leaf unit was 1. In the preceding example, the leaf unit was 1. A single digit is used to define each leaf. A single digit is used to define each leaf.

69. 69 Slide Example: Leaf Unit = 0.1 If we have data with values such as 8 9 10 11 Leaf Unit = 0.1 6 8 1 4 2 0 7 8.6 11.79.49.110.211.08.8 a stem-and-leaf display of these data will be

70. 70 Slide Example: Leaf Unit = 10 If we have data with values such as 16 17 18 19 Leaf Unit = 10 8 1 9 0 3 1 7 1806171719741791168219101838 a stem-and-leaf display of these data will be The 82 in 1682 is rounded down to 80 and is represented as an 8. The 82 in 1682 is rounded down to 80 and is represented as an 8.

71. 71 Slide Crosstabulations and Scatter Diagrams Crosstabulation and a scatter diagram are two Crosstabulation and a scatter diagram are two methods for summarizing the data for two variables methods for summarizing the data for two variables simultaneously. simultaneously. Often a manager is interested in tabular and Often a manager is interested in tabular and graphical methods that will help understand the graphical methods that will help understand the relationship between two variables. relationship between two variables. Thus far we have focused on methods that are used Thus far we have focused on methods that are used to summarize the data for one variable at a time. to summarize the data for one variable at a time.

72. 72 Slide Crosstabulation The left and top margin labels define the classes for The left and top margin labels define the classes for the two variables. the two variables. n Crosstabulation can be used when: One variable is Qualitative and the other is One variable is Qualitative and the other is Categorical, Categorical, Both variables are Qualitative, or Both variables are Qualitative, or Both variables are Categorical. Both variables are Categorical. A crosstabulation is a tabular summary of data for A crosstabulation is a tabular summary of data for two variables and helps to reveal the relationship between the two variables. two variables and helps to reveal the relationship between the two variables.

73. 73 Slide Price Range Colonial Log Split A-Frame Total < $99,000 > $99,000 18 6 19 12 55 45 30 20 35 15 Total 100 12 14 16 3 Home Style Home Style Crosstabulation Example: Finger Lakes Homes Example: Finger Lakes Homes quantitative variable variablequantitative categorical categorical The number of Finger Lakes homes sold for each style and price for the past two years is shown below.

74. 74 Slide Crosstabulation Insights Gained from Preceding Crosstabulation Only three homes in the sample are an A-Frame Only three homes in the sample are an A-Frame style and priced at more than $99,000. style and priced at more than $99,000. The greatest number of homes (19) in the sample The greatest number of homes (19) in the sample are a split-level style and priced at less than or are a split-level style and priced at less than or equal to $99,000. equal to $99,000. Example: Finger Lakes Homes Example: Finger Lakes Homes

75. 75 Slide PriceRange Colonial Log Split A-Frame Colonial Log Split A-Frame Total < $99,000 > $99,000 18 6 19 12 5545 30 20 35 15 Total 100 12 14 16 3 Home Style Home Style Crosstabulation Frequencydistribution for the price range variable Frequency distribution for the home style variable Example: Finger Lakes Homes Example: Finger Lakes Homes

76. 76 Slide Using Excel’s PivotTable Report to Create a Crosstabulation Excel Worksheet (showing partial data) Excel Worksheet (showing partial data) Note: Rows 10-101 are not shown.

77. 77 Slide Displaying the Initial PivotTable Field List and Displaying the Initial PivotTable Field List and PivotTable Report PivotTable Report Using Excel’s PivotTable Report to Create a Crosstabulation Step 1 Click the Insert tab on the Ribbon Step 2 In the Tables group, click the icon above the word PivotTable word PivotTable Step 3 When the Create PivotTable dialog box appears: Choose Select a Table or Range Choose Select a Table or Range Enter A1:C101 in the Table/Range box Enter A1:C101 in the Table/Range box Choose New Worksheet as the location for Choose New Worksheet as the location for the PivotTable Report the PivotTable Report Click OK Click OK

78. 78 Slide Setting Up the PivotTable Field List Setting Up the PivotTable Field List Using Excel’s PivotTable Report to Create a Crosstabulation Step 1 In the PivotTable Field List, go to Choose Fields to add to report to add to report Drag the Price ($) field to Row Labels area Drag the Price ($) field to Row Labels area Drag the Style field to Column Labels area Drag the Style field to Column Labels area Drag the Home field to the Values area Drag the Home field to the Values area Step 4 When the Value Field Settings dialog box appears: Under Summarize value field by, choose Count Under Summarize value field by, choose Count Choose New Worksheet as the location for Choose New Worksheet as the location for Click OK Click OK Step 2 Click on Sum of Home in the Values area Step 3 Click Value Field Settings from the list of options

79. 79 Slide Value Worksheet Value Worksheet Using Excel’s PivotTable Report to Create a Crosstabulation ABCDEFG 1 Count of HomeStyle 2Price ($)ColonialLogSplit-LevelA-FrameGrand Total 3 <=99K186191255 4 >99K121416345 5Grand Total30203515100 6

80. 80 Slide 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. Converting the entries in the table into row percentages or column percentages can provide additional insight about the relationship between the two variables.

81. 81 Slide PriceRange Colonial Log Split A-Frame Colonial Log Split A-Frame Total < $99,000 > $99,000 32.73 10.91 34.55 21.82 100100 Note: row totals are actually 100.01 due to rounding. 26.67 31.11 35.56 6.67 Home Style Home Style (Colonial and > $99K)/(All >$99K) x 100 = (12/45) x 100 Crosstabulation: Row Percentages Example: Finger Lakes Homes Example: Finger Lakes Homes

82. 82 Slide PriceRange Colonial Log Split A-Frame Colonial Log Split A-Frame < $99,000 > $99,000 60.00 30.00 54.29 80.00 40.00 70.00 45.71 20.00 Home Style Home Style 100 100 100 100 Total (Colonial and > $99K)/(All Colonial) x 100 = (12/30) x 100 Crosstabulation: Column Percentages Example: Finger Lakes Homes Example: Finger Lakes Homes

83. 83 Slide Crosstabulation: Simpson’s Paradox Simpson’ Paradox: In some cases the conclusions Simpson’ Paradox: In some cases the conclusions based upon an aggregated crosstabulation can be based upon an aggregated crosstabulation can be completely reversed if we look at the unaggregated completely reversed if we look at the unaggregated data. Before drawing conclusions about relationships between two variables (for aggregated data), you must investigate whether any hidden variables could affect the results. data. Before drawing conclusions about relationships between two variables (for aggregated data), you must investigate whether any hidden variables could affect the results. We must be careful in drawing conclusions about the We must be careful in drawing conclusions about the relationship between the two variables in the relationship between the two variables in the aggregated crosstabulation. aggregated crosstabulation. Data in two or more crosstabulations are often Data in two or more crosstabulations are often aggregated to produce a summary crosstabulation. aggregated to produce a summary crosstabulation.

84. 84 Slide The general pattern of the plotted points suggests the The general pattern of the plotted points suggests the overall relationship between the variables. overall relationship between the variables. One variable is shown on the horizontal axis and the One variable is shown on the horizontal axis and the other variable is shown on the vertical axis. other variable is shown on the vertical axis. A scatter diagram is a graphical presentation of the A scatter diagram is a graphical presentation of the relationship between two quantitative variables. relationship between two quantitative variables. Scatter Diagram and Trendline A trendline is an approximation of the relationship. A trendline is an approximation of the relationship.

85. 85 Slide Scatter Diagram A Positive Relationship A Positive Relationship x y

86. 86 Slide Scatter Diagram A Negative Relationship A Negative Relationship x y

87. 87 Slide Scatter Diagram No Apparent Relationship No Apparent Relationship x y

88. 88 Slide Example: Panthers Football Team Example: Panthers Football Team 1 3 2 1 3 14 24 18 17 30 x = Number of Interceptions y = Number of Points Scored Points Scored Scatter Diagram The Panthers football team is interested in The Panthers football team is interested in investigating the relationship, if any, between interceptions made and points scored.

89. 89 Slide Scatter Diagram y x Number of Interceptions Number of Points Scored 5 10 15 20 25 30 035 12304

90. 90 Slide Insights Gained from the Preceding Scatter Diagram Insights Gained from the Preceding Scatter Diagram The relationship is not perfect; all plotted points in The relationship is not perfect; all plotted points in the scatter diagram are not on a straight line. the scatter diagram are not on a straight line. Higher points scored are associated with a higher Higher points scored are associated with a higher number of interceptions. number of interceptions. The scatter diagram indicates a positive relationship The scatter diagram indicates a positive relationship between the number of interceptions and the between the number of interceptions and the number of points scored. number of points scored. Example: Panthers Football Team

91. 91 Slide Using Excel’s Chart Wizard to Construct a Scatter Diagram and Trendline Excel Worksheet (showing data) Excel Worksheet (showing data)

92. 92 Slide Step 1 Select cells A2:B6 Step 2 Click the Insert tab on the Excel Ribbon Step 3 In the Charts group, click Scatter Using Excel’s Chart Tools to Construct a Scatter Diagram and Trendline... continue Step 4 When the list of scatter diagram subtypes appears: Click Scatter with only Markers 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 Diagram for the Panthers Step 7 Select the Horizontal Axis (Value) Title and replace it with Number of Interceptions replace it with Number of Interceptions

93. 93 Slide Step 8 Select the Vertical (Value) Axis Title and replace it with Number of Points Scored it with Number of Points Scored Step 9 Right click Series 1 Legend Entry and click Delete Step 10 Position the pointer over any data point in the scatter diagram and right-click to display options scatter diagram and right-click to display options Using Excel’s Chart Tools to Construct a Scatter Diagram and Trendline Step 11 Choose Add Trendline Step 12 When the Format Trendline dialog box appears: Select Trendline Options Select Trendline Options Choose Linear from Trend/Regression Type list Choose Linear from Trend/Regression Type list Click Close Click Close - - - - - - - - - - - - - - - - To Add a Trendline - - - - - - - - - - - - - - -

94. 94 Slide Using Excel’s Chart Tools to Construct a Scatter Diagram and Trendline

95. 95 Slide Tabular and Graphical Methods Categorical Data Quantitative Data Tabular TabularMethods Methods Methods MethodsGraphical Methods MethodsGraphical Graphical Graphical Frequency Frequency Distribution Distribution Rel. Freq. Dist. Rel. Freq. Dist. Percent Freq. Percent Freq. Distribution Distribution Crosstabulation Crosstabulation Bar Graph Bar Graph Pie Chart Pie Chart Frequency Frequency Distribution Distribution Rel. Freq. Dist. Rel. Freq. Dist. % Freq. Dist. % Freq. Dist. Cum. Freq. Dist. Cum. Freq. Dist. Cum. Rel. Freq. Cum. Rel. Freq. Distribution Distribution Cum. % Freq. Cum. % Freq. Distribution Distribution Crosstabulation Crosstabulation Dot Plot Dot Plot Histogram Histogram Ogive Ogive Stem-and- Stem-and- Leaf Display Leaf Display Scatter Scatter Diagram Diagram DataData

96. 96 Slide End of Chapter 2, Part B