統計學. Fall 2014 授課教師 : 統計系余清祥 日期 :2014 年 9 月 30 日 第三週 : 敘述性統計量

Transcription

1 統計學 Fall 2014 授課教師 : 統計系余清祥 日期 :2014 年 9 月 30 日 第三週 : 敘述性統計量

2 基本資料分析 基本資料分析的首要目的在於資料偵錯 獲得資料的大略資訊 驗證已知結果 ( 例如 : 正常 vs. 異常!) 因此, 圖形 表格在基本資料分析中扮演重要的角色 ; 並由基本資料分析的結果中尋找合適的下一步分析方法 使用任何的統計方法前, 先確定該方法需要的假設條件是否滿足

3 圖形與表格 除了基本的敘述統計量外, 圖形與表格可以輔助判斷資料的特性 常見的圖形 :Boxplot Histogram 這些圖表看似簡單, 但仔細判讀仍可發現重要訊息, 甚至不需進階統計分析, 即能約略猜出分析的結論 本章先介紹圖形與表格, 下一章再介紹基本的敘述統計量 註 :A picture is worth a thousand words!

4 圖形有時描述地更傳神! Source:

5 Source:

6 STATISTICS in PRACTICE The Colgate-Palmolive Company uses statistics in its quality assurance program for home laundry detergent products. Customer concerns with the quantity of detergent in a carton. To control the problem, limits are placed on the acceptable range of powder density. Statistical samples are taken and the density of each powder sample is measured. Data summaries are then provided for operating personnel to keep the density within the desired quality. 6

7 Chapter 2, Part A Descriptive Statistics: Tabular and Graphical Displays Summarizing Data for a Categorical Variable Summarizing Data for a Quantitative Variable Categorical data use labels or names to identify categories of like items. Quantitative data are numerical values that indicate how much or how many. 7

8 2.1 Summarizing Categorical Data for a categorical Variable Frequency Distribution Relative Frequency Distribution Percent Frequency Distribution Bar Chart Pie Chart 8

9 Frequency Distribution -1 A frequency distribution is a tabular summary of data showing the number (frequency) of observations in each of several non-overlapping categories or classes. The objective is to provide insights about the data that cannot be quickly obtained by looking only at the original data. 9

10 Frequency Distribution -2 Example: Data from a sample of 50 Soft Drink Purchases 10

11 Frequency Distribution -3 Example: Frequency Distribution of Soft Drink Purchases 11

12 Frequency Distribution -4 Example: Marada Inn Guests staying at Marada Inn were asked to rate the quality of their accommodations as being excellent, above average, average, below average, or poor. Theratings provided by a sample of 20 guests are: Below Average Above Average Above Average Average Above Average Average Above Average Average Above Average Below Average Poor Excellent Above Average Average Above Average Above Average Below Average Poor Above Average Average 12

13 Frequency Distribution -5 Example: Marada Inn Rating Poor Below Average Average Above Average Excellent Frequency Total 20 13

14 Relative Frequency Distribution The relative frequency of a class is the fraction or proportion of the total number of data items belonging to the class. A relative frequency distribution is a tabular summary of a set of data showing the relative frequency for each class. 14

15 Percent Frequency Distribution The percent frequency of a class is the relative frequency multiplied by 100. A percent frequency distribution is a tabular summary of a set of data showing the percent frequency for each class. 15

16 Relative Frequency and Percent Frequency Distribution -1 Example: Relative and Percent Frequency Distribution of Soft Drink Purchases 16

17 Relative Frequency and Percent Frequency Distributions -2 Example: Marada Inn Relative Rating Frequency Poor.10 Below Average.15 Average.25 Above Average.45 Excellent.05 Total 1.00 Percent Frequency (100) = /20 =.05 17

18 Bar Chart -1 A bar chart is a graphical display for depicting qualitative data. On one axis (usually the horizontal axis), we specify the labels that are used for each of the classes. A frequency, relative frequency, or percent frequency scale can be used for the other axis (usually the vertical axis). Using a bar of fixed width drawn above each class label, we extend the height appropriately. The bars are separated to emphasize the fact that each class is a separate category. 18

19 Bar Chart -2 Example: Bar Graph of Soft Drink Purchases 19

20 Bar Chart -3 Example: Marada Inn Frequency 10 Marada Inn Quality Ratings Poor Below Average Average Above Average Excellent Rating 20

21

22

23 Pareto Diagram In quality control, bar charts are used to identify the most important causes of problems. When the bars are arranged in descending order of height from left to right (with the most frequently occurring cause appearing first) the bar chart is called a Pareto diagram. This diagram is named for its founder, Vilfredo Pareto, an Italian economist. 23

24 urce: (Excel

25 Pie Chart -1 The pie chart is a commonly used graphical display for presenting relative frequency and percent frequency distributions for categorical data. First draw a circle; then use the relative frequencies to subdivide the circle into sectors that correspond to the relative frequency for each class. Since there are 360 degrees in a circle, a class with a relative frequency of 0.25 would consume 0.25(360) = 90 degrees of the circle. 25

26 Pie Chart -2 Example: Pie Chart of Soft Drink Purchases 26

27 Example: Marada Inn Pie Chart -3 Marada Inn Quality Ratings Excellent 5% Above Average 45% Poor 10% Below Average 15% Average 25% 27

28 3-D Pie Chart Example: Pie Chart of Soft Drink Purchases 28

29 Example: Marada Inn Insights Gained from the Preceding Pie Chart One-half of the customers surveyed gave Marada a quality rating of above average or excellent (looking at the left side of the pie). This might please the manager. For each customer who gave an excellent rating, there were two customers who gave a poor rating (looking at the top of the pie). This should displease the manager. 29

30 2.2 Summarizing Quantitative Data Frequency Distribution Relative Frequency and Percent Frequency Distributions Dot Plot Histogram Cumulative Distributions Stem-and-Leaf Displays 30

31 Frequency Distribution -1 The three steps necessary to define the classes for a frequency distribution with quantitative data are: 1. Determine the number of non-overlapping classes. 2. Determine the width of each class. 3. Determine the class limits. 31

32 Frequency Distribution -2 Guidelines for Determining the Number of Classes Use between 5 and 20 classes. we recommend using between 5 and 20 classes. Data sets with a larger number of elements usually require a larger number of classes. Smaller data sets usually require fewer classes. The goal is to use enough classes to show the variation in the data, but not so many classes that some contain only a few data items. 32

33 Frequency Distribution -3 Guidelines for Determining the Width of Each Class Use classes of equal width. Approximate Class Width = Largest Data Value Smallest Data Value Number of Classes Making the classes the same width reduces the chance of inappropriate interpretations. 33

34 Frequency Distribution -4 Note on Number of Classes and Class Width In practice, the number of classes and the appropriate class width are determined by trial and error. Once a possible number of classes is chosen, the appropriate class width is found. The process can be repeated for a different number of classes. Ultimately, the analyst uses judgment to determine the combination of the number of classes and class width that provides the best frequency distribution for summarizing the data. 34

35 Frequency Distribution -5 Guidelines for Determining the Class Limits Class limits must be chosen so that each data item belongs to one and only one class. The lower class limit identifies the smallest possible data value assigned to the class. The upper class limit identifies the largest possible data value assigned to the class. The appropriate values for the class limits depend on the level of accuracy of the data. An open-end class requires only a lower class limit or an upper class limit. 35

36 Frequency Distribution -6 Example: These data show the time in days required to complete year-end audits for a sample of 20 clients of Sanderson and Clifford, a small public accounting firm with the data rounded to the nearest day. 36

37 Frequency Distribution -7 Example: Year-end audit times 1. Number of classes = 5 2. An approximate class width of (33 12)/5= We therefore decided to round up and use a class width of 5 days in the frequency distribution. 4. Frequency Distribution 37

38 Relative Frequency and Percent Frequency Distributions Example: Year-end audit times 38

39 Frequency Distribution -1 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. 39

40 Frequency Distribution -2 Example: Hudson Auto Repair Sample of Parts Cost($) for 50 Tune-ups 40

41 Frequency Distribution -3 Example: Hudson Auto Repair If we choose six classes: Approximate Class Width = (109-52)/6 = Parts Cost ($) Frequency Total 50 41

42 Relative Frequency and Percent Frequency Distributions -1 Example: Hudson Auto Repair Parts Cost ($) Relative Frequency Percent Frequency / (100) Total Percent frequency is the relative frequency multiplied by

43 Relative Frequency and Percent Frequency Distributions -2 Example: Hudson Auto Repair Insights Gained from the % Frequency Distribution: Only 4% of the parts costs are in the $50-59 class. 30% of the parts costs are under $70. The greatest percentage (32% or almost one-third) of the parts costs are in the $70-79 class. 10% of the parts costs are $100 or more. 43

44 Dot Plot -1 One of the simplest graphical summaries of data is a dot plot. A horizontal axis shows the range of data values. Then each data value is represented by a dot placed above the axis. Example: Dot Plot for The Audit Time Data 44

45 Dot Plot -2 Example: Hudson Auto Repair Tune-up Parts Cost Cost ($) 45

46 Histogram -1 Another common graphical display of quantitative data is a histogram( 直方圖 ). The variable of interest is placed on the horizontal axis. A rectangle is drawn above each class interval with its height corresponding to the interval s frequency, relative frequency, or percent frequency. Unlike a bar graph, a histogram has no natural separation between rectangles of adjacent classes. 46

47 Histogram -2 Example: Histogram for The Audit Time Data 47

48 Histogram -3 Example: Hudson Auto Repair Tune-up Parts Cost Frequency Parts Cost ($) 48

49 Histograms Showing Skewness -1 Histograms Showing Differing Levels of Skewness 49

50 Histograms Showing Skewness -2 Histogram provides information about the shape. Symmetric Left tail is the mirror image of the right tail Examples: Heights of People Relative Frequency

51 Histograms Showing Skewness -3 Moderately Skewed Left A longer tail to the left Example: Exam Scores Relative Frequency

52 Histograms Showing Skewness -4 Moderately Right Skewed A Longer tail to the right Example: Housing Values Relative Frequency

53 Histograms Showing Skewness -5 Highly Skewed Right A very long tail to the right Example: Executive Salaries Relative Frequency

54 Cumulative Distributions -1 Cumulative frequency distribution( 累積次數分配 ) - shows the number of items with values less than or equal to the upper limit of each class.. Cumulative relative frequency distribution shows the proportion of items with values less than or equal to the upper limit of each class. Cumulative percent frequency distribution shows the percentage of items with values less than or equal to the upper limit of each class. 54

55 Cumulative Distributions -2 The last entry in a cumulative frequency distribution always equals the total number of observations. The last entry in a cumulative relative frequency distribution always equals The last entry in a cumulative percent frequency distribution always equals

56 Example: Cumulative Distributions -3 Cumulative Frequency, Cumulative Relative Frequency and Cumulative Percent Frequency Distributions for the Audit Data. 56

57 Cumulative Distributions -4 Example: Hudson Auto Repair Cost ($) < 59 < 69 < 79 < 89 < 99 < 109 Cumulative Frequency Cumulative Relative Frequency Cumulative Percent Frequency /50.30(100 57

58 Stem-and-Leaf Display -1 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. 58

59 Stem-and-Leaf Display -2 Example: Number of Questions Answered Correctly 59

60 Stem-and-Leaf Display -3 Stem : The numbers to the left of the vertical line (6, 7, 8, 9, 10, 11, 12, 13, and 14). Leaf : each digit to the right of the vertical line. 60

61 Stem-and-Leaf Display -4 Although the stem-and-leaf display may appear to offer the same information as a histogram, it has two primary advantages. 1. The stem-and-leaf display is easier to construct by hand. 2. Within a class interval, the stem-and-leaf display provides more information than the histogram because the stem-and-leaf shows the actual data. 61

62 Stem-and-Leaf Display -5 Rotating the original stem-and-leaf display counterclockwise onto its side provides a picture of the data that is similar to a histogram with classes of 60 69, 70 79, 80 89, etc. 62

63 Stem-and-Leaf Display -6 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. 63

64 Stem-and-Leaf Display -7 Example: Hudson Auto Repair Sample of Parts Cost ($) for 50 Tune-ups 64

65 Stem-and-Leaf Display -8 Example: Hudson Auto Repair a stem a leaf 65

66 Stretched Stem-and-Leaf Display -9 If we believe the original stem-and-leaf display has condensed the data too much, we can stretch the display vertically 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

67 Stem-and-Leaf Display -10 Example: Number of Questions Answered Correctly on An Aptitude Test 67

68 Stretched Stem-and-Leaf Display -11 Example: Hudson Auto Repair

69 Leaf Units Stem-and-Leaf Display -12 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. 69

70 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 =

71 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. 71

72

73 End of Chapter 2, Part A 73

74 Chapter 2, Part B Descriptive Statistics: Tabular and Graphical Displays Summarizing Data for Two Variables Using Tables Summarizing Data for Two Variables Using Graphical Displays Data Visualization: Best Practices in Creating Effective Graphical Displays 74

75 2.3 Summarizing Data for Two Variables Using Tables -1 Crosstabulation Simpson s Paradox 75

76 Summarizing Data for Two Variables Using Tables -2 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 is a method for summarizing the data for two variables. 76

77 Crosstabulation -1 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. 77

78 Crosstabulation -2 Example: Data from Zagat s Restaurant Review Data on a restaurant s quality rating and typical meal price are reported. Quality rating is a qualitative variable with rating categories of good, very good, and excellent. Meal price is a quantitative variable that ranges from $10 to $49. 78

79 Crosstabulation -3 Example: : Data from Zagat s Restaurant The data for the first 10 restaurants 79

80 Crosstabulation -4 Example: Data from Zagat s Restaurant Crosstabulation of Quality Rating and Meal Price for 300 Los Angeles Restaurants 80

81 Crosstabulation -5 Example: Data from Zagat s Restaurant Insights Gained from Preceding Crosstabulation 1. The greatest number of restaurants in the sample (64) have a very good rating and a meal price in the $20 29 range. 2. Only two restaurants have an excellent rating and a meal price in the $10 19 range. 3. In the right margin, data on quality ratings show 84 restaurants with a good quality rating, 150 restaurants with a very good quality rating, and 66 restaurants with an excellent quality rating. 81

82 Crosstabulation: Row or Column Percentages -1 Example: Data from Zagat s Restaurant Converting the entries in the table into row percentages or column percentages can provide additional insight about the relationship between the two variables. 82

83 Crosstabulation: Row or Column Percentages -2 Example: Data from Zagat s Restaurant Relative and Percent Frequency Distribution for the Quality Rating Variable (column). 83

84 Crosstabulation: Row or Column Percentages -3 Example: Data from Zagat s Restaurant Relative and Percent Frequency Distribution for The Meal Price Variable (row). 84

85 Crosstabulation -6 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

86 Crosstabulation -7 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. 86

87 Crosstabulation -8 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 87

88 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

89 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

90 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. In some cases the conclusions based upon an aggregated crosstabulation can be completely reversed if we look at the unaggregated data. The reversal of conclusions based on aggregate and unaggregated data is called Simpson s paradox. 90

91 Simpson's paradox for continuous data: a positive trend appears for two separate groups (blue and red), a negative trend (black, dashed) appears when the data are combined.

92 列聯表的資訊 美國某州的婦運團體研究判刑的輕重是否存有性別歧視, 隨機抽取男女各一百名判刑確定的嫌犯, 結果如下 : 輕刑重刑總數 男嫌疑犯 女嫌疑犯

93 2.4 Summarizing Data for Two Variables Using Graphical Displays -1 Scatter Diagram and Trendline Side-by-Side and Stacked Bar Chart 93

94 Summarizing Data for Two Variables Using Graphical Displays -2 In most cases, a graphical display is more useful than a table for recognizing patterns and trends. Displaying data in creative ways can lead to powerful insights. Scatter diagrams and trendlines are useful in exploring the relationship between two variables. 94

95 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. 95

96 Scatter Diagram -1 A Positive Relationship y x 96

97 Scatter Diagram -2 A Negative Relationship y x 97

98 Scatter Diagram -3 No Apparent Relationship y x 98

99 Scatter Diagram -4 Example: The Stereo and Sound Equipment Store Consider the advertising/sales relationship for a stereo and sound equipment store in San Francisco. On 10 occasions during the past three months. 99

100 Scatter Diagram -5 Example: Scatter Diagram and Trendline for The Stereo and Sound Equipment Store. 100

101 Scatter Diagram -6 The scatter diagram indicates a positive relationship between the number of commercials and sales. Higher sales are associated with a higher number of commercials. The relationship is NOT perfect in that all points are not on a straight line. However, the general pattern of the points and the trendline suggest that the overall relationship is positive. The equation of the trendline is y = x. The slope of the trendline is 4.95 and the y- intercept is

102 Scatter Diagram -7 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

103 Scatter Diagram and Trendline Example: Panthers Football Team Number of Points Scored y Number of Interceptions x 103

104 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. 104

105 Side-by-Side Bar Chart -1 A side-by-side bar chart is a graphical display for depicting multiple bar charts on the same display. Each cluster of bars represents one value of the first variable. Each bar within a cluster represents one value of the second variable. 105

106 Side-by-Side Bar Chart -2 Example: side-by-side bar chart for the quality rating and meal price data 106

107 Side-by-Side Bar Chart -3 Frequency Finger Lake Homes Colonial Log Split-Level A-Frame < $200,000 > $200,000 Home Style 107

108 Stacked Bar Chart -1 A stacked bar chart is another way to display and compare two variables on the same display. It is a bar chart in which each bar is broken into rectangular segments of a different color. If percentage frequencies are displayed, all bars will be of the same height (or length), extending to the 100% mark. 108

109 Stacked Bar Chart -2 Example: Column Percentages for Each Meal Price Category 109

110 Stacked Bar Chart -3 Example: Stacked Bar Chart for Quality Rating and Meal Price Data 110

111 Stacked Bar Chart -4 Frequency Finger Lake Homes Colonial Log Split A-Frame < $200,000 > $200,000 Home Style 111

112 2.5 Data Visualization: Best Practices in Creating Effective Graphical Displays -1 Creating Effective Graphical Displays Choosing the Type of Graphical Display Data Dashboards Data Visualization in Practice: Cincinnati Zoo and Botanical Garden 112

113 Data Visualization: Best Practices in Creating Effective Graphical Displays -2 Data visualization describes the use of graphical displays to summarize and present information about a data set. The goal is to communicate as effectively and clearly as possible the key information about the data. 113

114 Creating Effective Graphical Displays -1 Creating effective graphical displays is as much art as it is science. Here are some guidelines Give the display a clear and concise title. Keep the display simple. Do not use three dimensions when two dimensions are sufficient. Clearly label each axis and provide the units of measure. If colors are used, make sure they are distinct. If multiple colors or lines are used, provide a legend. 114

115 Creating Effective Graphical Displays -2 Example: the forecasted or planned value of sales ($1000s) and the actual value of sales ($1000s) by sales region in the United States for Gustin Chemical for the past year. 115

116 Creating Effective Graphical Displays -3 Example: Side-by-Side Bar Chart for Planned Versus Actual Sales 116

117 Choosing the Type of Graphical Display Displays used to show the distribution of data: Bar Chart Pie Chart Dot Plot Histogram Stem-and-Leaf Display Displays used to make comparisons: Side-by-Side Bar Chart Stacked Bar Chart Displays used to show relationships: Scatter Diagram Trendline 117

118 Data Dashboards -1 A data dashboard is a widely used data visualization tool. It organizes and presents Key Performance Indicators (KPIs) used to monitor an organization or process. It provides timely, summary information that is easy read, understand, and interpret. Some additional guidelines include Minimize the need for screen scrolling. Avoid unnecessary use of color or 3D. Use borders between charts to improve readability. 118

119 Data Dashboards -2 Example: a car s speed, fuel level, engine temperature, and oil level are important information to monitor in a car. Example: KPIs are inventory on hand, daily sales, percentage of on-time deliveries, and sales revenue per quarter. A data dashboard should provide timely summary information (potentially from various sources) on KPIs that is important to the user, and it should do so in a manner that informs rather than overwhelms its user. 119

120 Data Dashboards -3 Example: Grogan Oil Information Technology Call Center Data Dashboard. 120

121 Data Dashboards -4 The data dashboard was developed to monitor the performance of the call center. This data dashboard combines several displays to monitor the call center s KPIs. The data presented the current shift, which started at 8:00 A.M. The stacked bar chart the call volume for each type of problem over time. The pie chart shows the percentage of time that callcenter employees spent on each type of problem or not working on a call (idle). 121

122 Data Visualization in Practice -1 Data Dashboard for The Cincinnati Zoo 122

123 Data Visualization in Practice -2 Zoo management to track the following key performance indicators: Item Analysis (sales volumes and sales dollars by location within the zoo) Geo Analytics (maps and displays of where the day s visitors are spending their time at the zoo) Customer Spending Cashier Sales Performance Sales and Attendance Data versus Weather Patterns Performance of the Zoo s Loyalty Rewards Program 123

124 Data Visualization in Practice -3 The Cincinnati Zoo ipad Data Dashboard 124

125 Data Visualization in Practice -4 The Cincinnati Zoo s ipad data dashboard provides managers with access to the following information: Real-time attendance data, including what types ofguests are coming to the zoo Real-time analysis showing which items are selling the fastest inside the zoo Real-time geographical representation of where the zoo s visitors live The system has been directly responsible for revenue growth, increased visitation to the zoo, enhanced customer service, and reduced marketing costs. 125

126 Tabular and Graphical Displays Data Categorical Data Quantitative Data Tabular Displays Graphical Displays Tabular Displays Graphical Displays Frequency Distribution Rel. Freq. Dist. Percent Freq. Distribution Crosstabulation Bar Chart Pie Chart Side-by-Side Bar Chart Stacked Bar Chart Frequency Distribution Rel. Freq. Dist. % Freq. Dist. Cum. Freq. Dist. Cum. Rel. Freq. Distribution Cum. % Freq. Distribution Crosstabulation Dot Plot Histogram Stem-and- Leaf Display Scatter Diagram 126

127 End of Chapter 2, Part B 127