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1、Organizing and Visualizing Variables,Chapter 2,Organizing and Visualizing Var,Objectives,In this chapter you learn: Methods to organize variables.Methods to visualize variables.Methods to organize or visualize more than one variable at the same time.Principles of proper visualizations.,ObjectivesIn
2、this chapter you,Categorical Data Are Organized By Utilizing Tables,DCOVA,Categorical Data Are Organized,Organizing Categorical Data: Summary Table,A summary table tallies the frequencies or percentages of items in a set of categories so that you can see differences between categories.,DCOVA,Main Re
3、ason Young Adults Shop Online,Source: Data extracted and adapted from “Main Reason Young Adults Shop Online?”USA Today, December 5, 2012, p. 1A.,Organizing Categorical Data: S,A Contingency Table Helps Organize Two or More Categorical Variables,Used to study patterns that may exist between the respo
4、nses of two or more categorical variablesCross tabulates or tallies jointly the responses of the categorical variablesFor two variables the tallies for one variable are located in the rows and the tallies for the second variable are located in the columns,DCOVA,A Contingency Table Helps Orga,Conting
5、ency Table - Example,A random sample of 400 invoices is drawn.Each invoice is categorized as a small, medium, or large amount.Each invoice is also examined to identify if there are any errors.This data are then organized in the contingency table to the right.,DCOVA,Contingency Table ShowingFrequency
6、 of Invoices CategorizedBy Size and The Presence Of Errors,Contingency Table - ExampleA r,Contingency Table Based On Percentage Of Overall Total,DCOVA,42.50% = 170 / 40025.00% = 100 / 40016.25% = 65 / 400,83.75% of sampled invoices have no errors and 47.50% of sampled invoices are for small amounts.
7、,Contingency Table Based On Per,Contingency Table Based On Percentage of Row Totals,DCOVA,89.47% = 170 / 19071.43% = 100 / 14092.86% = 65 / 70,Medium invoices have a larger chance (28.57%) of having errors than small (10.53%) or large (7.14%) invoices.,Contingency Table Based On Per,Contingency Tabl
8、e Based On Percentage Of Column Totals,DCOVA,50.75% = 170 / 33530.77% = 20 / 65,There is a 61.54% chance that invoices with errors are of medium size.,Contingency Table Based On Per,Tables Used For Organizing Numerical Data,DCOVA,Tables Used For Organizing Nu,Organizing Numerical Data: Ordered Array
9、,An ordered array is a sequence of data, in rank order, from the smallest value to the largest value.Shows range (minimum value to maximum value)May help identify outliers (unusual observations),DCOVA,Organizing Numerical Data: Or,Organizing Numerical Data: Frequency Distribution,The frequency distr
10、ibution is a summary table in which the data are arranged into numerically ordered classes. You must give attention to selecting the appropriate number of class groupings for the table, determining a suitable width of a class grouping, and establishing the boundaries of each class grouping to avoid
11、overlapping.The number of classes depends on the number of values in the data. With a larger number of values, typically there are more classes. In general, a frequency distribution should have at least 5 but no more than 15 classes.To determine the width of a class interval, you divide the range (H
12、ighest valueLowest value) of the data by the number of class groupings desired.,DCOVA,Organizing Numerical Data: Fr,Organizing Numerical Data: Frequency Distribution Example,Example: A manufacturer of insulation randomly selects 20 winter days and records the daily high temperature24, 35, 17, 21, 24
13、, 37, 26, 46, 58, 30, 32, 13, 12, 38, 41, 43, 44, 27, 53, 27,DCOVA,Organizing Numerical Data: Fr,Organizing Numerical Data: Frequency Distribution Example,Sort raw data in ascending order:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58Find range: 58 - 12 = 46Select num
14、ber of classes: 5 (usually between 5 and 15)Compute class interval (width): 10 (46/5 then round up)Determine class boundaries (limits):Class 1: 10 but less than 20Class 2: 20 but less than 30Class 3: 30 but less than 40Class 4: 40 but less than 50Class 5: 50 but less than 60Compute class midpoints:
15、15, 25, 35, 45, 55Count observations & assign to classes,DCOVA,Organizing Numerical Data: Fr,Organizing Numerical Data: Frequency Distribution Example,Data in ordered array:12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58,DCOVA,Organizing Numerical Data: Fre,Organizing
16、Numerical Data: Relative & Percent Frequency Distribution Example,DCOVA,Relative Frequency = Frequency / Total, e.g. 0.10 = 2 / 20,Organizing Numerical Data: Rel,Organizing Numerical Data: Cumulative Frequency Distribution Example,Class,10 but less than 20 3 15% 3 15%20 but less than 30 6 30% 9 45%3
17、0 but less than 40 5 25% 14 70%40 but less than 50 4 20% 18 90%50 but less than 60 2 10% 20 100% Total 20 100 20100%,Percentage,Cumulative Percentage,Cumulative Percentage = Cumulative Frequency / Total * 100 e.g. 45% = 100*9/20,Frequency,Cumulative Frequency,DCOVA,Organizing Numerical Data: Cum,Why
18、 Use a Frequency Distribution?,It condenses the raw data into a more useful formIt allows for a quick visual interpretation of the dataIt enables the determination of the major characteristics of the data set including where the data are concentrated / clustered,DCOVA,Why Use a Frequency Distributi,
19、Frequency Distributions:Some Tips,Different class boundaries may provide different pictures for the same data (especially for smaller data sets)Shifts in data concentration may show up when different class boundaries are chosenAs the size of the data set increases, the impact of alterations in the s
20、election of class boundaries is greatly reducedWhen comparing two or more groups with different sample sizes, you must use either a relative frequency or a percentage distribution,DCOVA,Frequency Distributions:Some,Visualizing Categorical Data Through Graphical Displays,DCOVA,Visualizing Categorical
21、 Data T,Visualizing Categorical Data: The Bar Chart,The bar chart visualizes a categorical variable as a series of bars. The length of each bar represents either the frequency or percentage of values for each category. Each bar is separated by a space called a gap.,DCOVA,Visualizing Categorical Data
22、:,Visualizing Categorical Data: The Pie Chart,The pie chart is a circle broken up into slices that represent categories. The size of each slice of the pie varies according to the percentage in each category.,DCOVA,Visualizing Categorical Data:,Visualizing Categorical Data:The Pareto Chart,Used to po
23、rtray categorical dataA vertical bar chart, where categories are shown in descending order of frequencyA cumulative polygon is shown in the same graphUsed to separate the “vital few” from the “trivial many”,DCOVA,Visualizing Categorical Data:,Visualizing Categorical Data:The Pareto Chart (cont),DCOV
24、A,CumulativeCause Frequency PercentPercentWarped card jammed 365 50.41% 50.41%Card unreadable 234 32.32% 82.73%ATM malfunctions32 4.42% 87.15%ATM out of cash28 3.87% 91.02%Invalid amount requested 23 3.18% 94.20%Wrong keystroke 23 3.18% 97.38%Lack of funds in account 19 2.62%100.00%Total 724 100.00%
25、Source: Data extracted from A. Bhalla, “Dont Misuse the Pareto Principle,” Six Sigma ForumMagazine, May 2009, pp. 1518.,Ordered Summary Table For CausesOf Incomplete ATM Transactions,Visualizing Categorical Data:,Visualizing Categorical Data:The Pareto Chart (cont),DCOVA,The “VitalFew”,Visualizing C
26、ategorical Data:,Visualizing Categorical Data:Side By Side Bar Charts,The side by side bar chart represents the data from a contingency table.,DCOVA,Invoices with errors are much more likely to be ofmedium size (61.54% vs 30.77% and 7.69%),Visualizing Categorical Data:,Visualizing Numerical Data By
27、Using Graphical Displays,DCOVA,Visualizing Numerical Data By,Stem-and-Leaf Display,A simple way to see how the data are distributed and where concentrations of data existMETHOD: Separate the sorted data series into leading digits (the stems) and the trailing digits (the leaves),DCOVA,Stem-and-Leaf D
28、isplayA simple,Organizing Numerical Data: Stem and Leaf Display,A stem-and-leaf display organizes data into groups (called stems) so that the values within each group (the leaves) branch out to the right on each row.,Age of College Students Day Students Night Students,DCOVA,Organizing Numerical Data
29、: St,Visualizing Numerical Data: The Histogram,A vertical bar chart of the data in a frequency distribution is called a histogram.In a histogram there are no gaps between adjacent bars. The class boundaries (or class midpoints) are shown on the horizontal axis.The vertical axis is either frequency,
30、relative frequency, or percentage.The height of the bars represent the frequency, relative frequency, or percentage.,DCOVA,Visualizing Numerical Data: T,Visualizing Numerical Data: The Histogram,(In a percentage histogram the vertical axis would be defined to show the percentage of observations per
31、class),DCOVA,Visualizing Numerical Data: T,Visualizing Numerical Data: The Polygon,A percentage polygon is formed by having the midpoint of each class represent the data in that class and then connecting the sequence of midpoints at their respective class percentages. The cumulative percentage polyg
32、on, or ogive, displays the variable of interest along the X axis, and the cumulative percentages along the Y axis.Useful when there are two or more groups to compare.,DCOVA,Visualizing Numerical Data: T,Visualizing Numerical Data: The Percentage Polygon,DCOVA,Useful When Comparing Two or More Groups
33、,Visualizing Numerical Data: T,Visualizing Numerical Data: The Percentage Polygon,DCOVA,Visualizing Numerical Data: T,Visualizing Two Numerical Variables By Using Graphical Displays,DCOVA,Visualizing Two Numerical Vari,Visualizing Two Numerical Variables: The Scatter Plot,Scatter plots are used for
34、numerical data consisting of paired observations taken from two numerical variablesOne variable is measured on the vertical axis and the other variable is measured on the horizontal axisScatter plots are used to examine possible relationships between two numerical variables,DCOVA,Visualizing Two Num
35、erical Vari,Scatter Plot Example,DCOVA,Scatter Plot ExampleVolume per,A Time-Series Plot is used to study patterns in the values of a numeric variable over timeThe Time-Series Plot:Numeric variable is measured on the vertical axis and the time period is measured on the horizontal axis,Visualizing Tw
36、o Numerical Variables: The Time Series Plot,DCOVA,A Time-Series Plot is used to,Time Series Plot Example,DCOVA,Time Series Plot ExampleYearNu,A multidimensional contingency table is constructed by tallying the responses of three or more categorical variables.In Excel creating a Pivot Table to yield
37、an interactive display of this type.While Minitab will not create an interactive table, it has many specialized statistical & graphical procedures (not covered in this book) to analyze & visualize multidimensional data.,Organizing Many Categorical Variables: The Multidimensional Contingency Table,DC
38、OVA,A multidimensional contingency,Using Excel Pivot Tables To Organize & Visualize Many Variables,A pivot table:Summarizes variables as a multidimensional summary tableAllows interactive changing of the level of summarization and formatting of the variablesAllows you to interactively “slice” your d
39、ata to summarize subsets of data that meet specified criteriaCan be used to discover possible patterns and relationships in multidimensional data that simpler tables and charts would fail to make apparent.,DCOVA,Using Excel Pivot Tables To Or,A Multidimensional Contingency Table Tallies Responses Of
40、 Three or More Categorical Variables,Two Dimensional Table Showing The Mean 10 Year Return % Broken Out By Type Of Fund & Risk Level,DCOVA,Three Dimensional Table Showing The Mean 10 Year Return % Broken Out By Type Of Fund, Market Cap, &Risk Level,A Multidimensional Contingency,Data Discovery Metho
41、ds Can Yield Initial Insights Into Data,Data discovery are methods enable the performance of preliminary analyses by manipulating interactive summarizationsAre used to:Take a closer look at historical or status dataReview data for unusual valuesUncover new patterns in dataDrill-down is perhaps the s
42、implest form of data discovery,DCOVA,Data Discovery Methods Can Yie,Drill-Down Reveals The Data Underlying A Higher-Level Summary,DCOVA,Results of drilling down to the details about smallmarket cap value funds withlow risk.,Drill-Down Reveals The Data Un,Some Data Discovery Methods Are Primarily Vis
43、ual,A treemap is such a methodA treemap visualizes the comparison of two or more variables using the size and color of rectangles to represent valuesWhen used with one or more categorical variables it forms a multilevel hierarchy or tree that can uncover patterns among numerical variables.,DCOVA,Som
44、e Data Discovery Methods Ar,An Example Of A Treemap,DCOVA,A treemap of the numerical variables assets (size) and 10-yearreturn percentage (color) for growth and value funds that havesmall market capitalizations and low risk,An Example Of A TreemapDCOVAA,The Challenges in Organizing and Visualizing V
45、ariables,When organizing and visualizing data need to be mindful of:The limits of others ability to perceive and comprehendPresentation issues that can undercut the usefulness of methods from this chapter.It is easy to create summaries thatObscure the data orCreate false impressions,DCOVA,The Challe
46、nges in Organizing a,An Example Of Obscuring Data, Information Overload,DCOVA,An Example Of Obscuring Data,False Impressions Can Be Created In Many Ways,Selective summarizationPresenting only part of the data collectedImproperly constructed chartsPotential pie chart issuesImproperly scaled axesA Y a
47、xis that does not begin at the origin or is a broken axis missing intermediate valuesChartjunk,DCOVA,False Impressions Can Be Creat,An Example of Selective Summarization, These Two Summarizations Tell Totally Different Stories,DCOVA,An Example of Selective Summar,How Obvious Is It That Both Pie Char
48、ts Summarize The Same Data?,DCOVA,Why is it hard to tell? What would you do to improve?,How Obvious Is It That Both Pi,Graphical Errors: No Relative Basis,As received by students.,As received by students.,Bad Presentation,0,200,300,FR,SO,JR,SR,Freq.,10%,30%,FR,SO,JR,SR,FR = Freshmen, SO = Sophomore,
49、 JR = Junior, SR = Senior,100,20%,0%,%,Good Presentation,DCOVA,Graphical Errors: No Relative,Graphical Errors: Compressing the Vertical Axis,Good Presentation,Quarterly Sales,Quarterly Sales,Bad Presentation,0,25,50,Q1,Q2,Q3,Q4,$,0,100,200,Q1,Q2,Q3,Q4,$,DCOVA,Graphical Errors: Compressing,Graphical
50、Errors: No Zero Point on the Vertical Axis,Monthly Sales,36,39,42,45,J,F,M,A,M,J,$,Graphing the first six months of sales,Monthly Sales,0,39,42,45,J,F,M,A,M,J,$,36,Good Presentations,Bad Presentation,DCOVA,Graphical Errors: No Zero Poin,Graphical Errors: Chart Junk, Can You Identify The Junk?,DCOVA,
