1 1 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. SLIDES. BY John Loucks St. Edward’s University

2 2 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Chapter 2, Part B Descriptive Statistics: Tabular and Graphical Displays n Summarizing Data for Two Variables Using Graphical Displays Using Graphical Displays n Summarizing Data for Two Variables Using Tables Using Tables n Data Visualization: Best Practices in Creating Effective Graphical Displays Effective Graphical Displays

3 3 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Summarizing Data for Two Variables Using Tables Crosstabulation is a method for summarizing the Crosstabulation is a method for summarizing the data for two variables. 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.

4 4 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. 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. Crosstabulation can be used when: Crosstabulation can be used when: one variable is categorical and the other is one variable is categorical and the other is quantitative, quantitative, both variables are categorical, or both variables are categorical, or both variables are quantitative. both variables are quantitative. A crosstabulation is a tabular summary of data for A crosstabulation is a tabular summary of data for two variables. two variables.

5 5 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Price Range Colonial Log Split A-Frame Total < $250,000 > $250, Total 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.

6 6 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. 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 $250,000 or more. style and priced at $250,000 or more. 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 are a split-level style and priced at less than $250,000. $250,000. Example: Finger Lakes Homes Example: Finger Lakes Homes

7 7 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. PriceRange Colonial Log Split A-Frame Colonial Log Split A-Frame Total < $250,000 > $250, Total Home Style Home Style Crosstabulation Frequencydistribution for the price range variableFrequencydistribution for the price range variable Frequency distribution for the home style variable Frequency distribution for the home style variable Example: Finger Lakes Homes Example: Finger Lakes Homes

8 8 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. 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.

9 9 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. PriceRange Colonial Log Split A-Frame Colonial Log Split A-Frame Total < $250,000 > $250, Note: row totals are actually due to rounding Home Style Home Style (Colonial and > $250K)/(All > $250K) x 100 = (12/45) x 100 Crosstabulation: Row Percentages Example: Finger Lakes Homes Example: Finger Lakes Homes

10 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. PriceRange Colonial Log Split A-Frame Colonial Log Split A-Frame < $250,000 > $250, Home Style Home Style Total (Colonial and > $250K)/(All Colonial) x 100 = (12/30) x 100 Crosstabulation: Column Percentages Example: Finger Lakes Homes Example: Finger Lakes Homes

11 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Crosstabulation: Simpson’s Paradox In some cases the conclusions based upon an In some cases the conclusions based upon an aggregated crosstabulation can be completely aggregated crosstabulation can be completely reversed if we look at the unaggregated data. The reversed if we look at the unaggregated data. The reversal of conclusions based on aggregate and reversal of conclusions based on aggregate and unaggregated data is called Simpson’s paradox. unaggregated data is called Simpson’s paradox. 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.

12 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Summarizing Data for Two Variables Using Graphical Displays Scatter diagrams and trendlines are useful in Scatter diagrams and trendlines are useful in exploring the relationship between two variables. Displaying data in creative ways can lead to powerful Displaying data in creative ways can lead to powerful insights. insights. In most cases, a graphical display is more useful than In most cases, a graphical display is more useful than a table for recognizing patterns and trends. a table for recognizing patterns and trends.

13 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. The general pattern of the plotted points suggests The general pattern of the plotted points suggests the overall relationship between the variables. the overall relationship between the variables. One variable is shown on the horizontal axis and One variable is shown on the horizontal axis and the other variable is shown on the vertical axis. the 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 provides an approximation of the A trendline provides an approximation of the relationship. relationship.

14 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Scatter Diagram A Positive Relationship A Positive Relationship x y

15 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Scatter Diagram A Negative Relationship A Negative Relationship x y

16 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Scatter Diagram No Apparent Relationship No Apparent Relationship x y

17 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Example: Panthers Football Team Example: Panthers Football Team 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.

18 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Scatter Diagram and Trendline y x Number of Interceptions Number of Points Scored

19 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. 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

20 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Side-by-Side Bar Chart Each bar within a cluster represents one value of Each bar within a cluster represents one value of the second variable. the second variable. Each cluster of bars represents one value of the Each cluster of bars represents one value of the first variable. first variable. A side-by-side bar chart is a graphical display for A side-by-side bar chart is a graphical display for depicting multiple bar charts on the same display. depicting multiple bar charts on the same display.

21 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Side-by-Side Bar Chart Colonial Log Split-Level A-Frame Frequency Home Style Finger Lake Homes < $250,000 > $250,000

22 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Stacked Bar Chart It is a bar chart in which each bar is broken into It is a bar chart in which each bar is broken into rectangular segments of a different color. rectangular segments of a different color. A stacked bar chart is another way to display and A stacked bar chart is another way to display and compare two variables on the same display. compare two variables on the same display. If percentage frequencies are displayed, all bars If percentage frequencies are displayed, all bars will be of the same height (or length), extending to will be of the same height (or length), extending to the 100% mark. the 100% mark.

23 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Stacked Bar Chart Colonial Log Split A-Frame Frequency Home Style Finger Lake Homes < $250,000 > $250,000 FrequenciesdisplayedFrequenciesdisplayed

24 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Stacked Bar Chart Colonial Log Split A-Frame Percentage Frequency Home Style Finger Lake Homes < $250,000 > $250,000 Percentage frequenciesdisplayed frequenciesdisplayed

25 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Data Visualization: Best Practices in Creating Effective Graphical Displays The goal is to communicate as effectively and clearly The goal is to communicate as effectively and clearly as possible the key information about the data. as possible the key information about the data. Data visualization describes the use of graphical Data visualization describes the use of graphical displays to summarize and present information displays to summarize and present information about a data set. about a data set.

26 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Creating Effective Graphical Displays Here are some guidelines... Here are some guidelines... Creating effective graphical displays is as much art Creating effective graphical displays is as much art as it is science. as it is science.  Give the display a clear and concise title.  If multiple colors or lines are used, provide a legend. legend.  Keep the display simple.  Clearly label each axis and provide the units of measure. measure.  If colors are used, make sure they are distinct.

27 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Choosing the Type of Graphical Display Displays used to show the distribution of data: Displays used to show the distribution of data: Bar Chart Pie Chart Stem-and-Leaf Display HistogramHistogram Dot Plot to show the frequency distribution or relative frequency distribution for categorical data to show the relative frequency or percent frequency for categorical data to show the distribution for quantitative data over the entire range of the data to show the frequency distribution for quantitative data over a set of class intervals to show both the rank order and shape of the distribution for quantitative data

28 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Displays used to make comparisons: Displays used to make comparisons: to compare two variables to compare the relative frequency or percent frequency of two categorical variables Choosing the Type of Graphical Display Side-by-Side Bar Chart Stacked Bar Chart

29 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Displays used to show relationships: Displays used to show relationships: to show the relationship between two quantitative variables to approximate the relationship of data in a scatter diagram Choosing the Type of Graphical Display TrendlineTrendline Scatter Diagram

30 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Data Dashboards It organizes and presents key performance indicators It organizes and presents key performance indicators (KPIs) used to monitor an organization or process. (KPIs) used to monitor an organization or process. A data dashboard is a widely used data A data dashboard is a widely used data visualization tool. visualization tool. It provides timely, summary information that is easy It provides timely, summary information that is easy to read, understand, and interpret. to 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. readability.

31 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Data Dashboard Example

32 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. Tabular and Graphical Displays Categorical Data Quantitative Data TabularDisplaysTabularDisplaysTabularDisplaysTabularDisplaysGraphical Displays DisplaysGraphical Graphical Graphical Frequency Frequency Distribution Distribution Rel. Freq. Dist. Rel. Freq. Dist. Percent Freq. Percent Freq. Distribution Distribution Crosstabulation Crosstabulation Bar Chart Bar Chart Pie Chart Pie Chart Side-by-Side Side-by-Side Bar Chart Bar Chart Stacked Stacked Bar Chart Bar 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 Stem-and- Stem-and- Leaf Display Leaf Display Scatter Scatter Diagram Diagram DataData

33 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. or duplicated, or posted to a publicly accessible website, in whole or in part. End of Chapter 2, Part B