© 2003 Prentice-Hall, Inc. Chapter 2 Presenting Data in Tables and Charts Business Statistics (9 th Edition)

© 2003 Prentice-Hall, Inc. Chapter Topics Guidelines to Analyze data Organizing Numerical Data The Ordered Array and Stem-Leaf Display Tabulating and Graphing Univariate Numerical Data Frequency Distributions: Tables, Histograms, Polygons Describing Distribution: Shape, Center and Spread Cumulative Distributions: Tables, the Ogive Graphing Bivariate Numerical Data

© 2003 Prentice-Hall, Inc. Chapter Topics Displaying Categorical Data Tabulating and Graphing Univariate Categorical Data The Summary Table Bar and Pie Charts, the Pareto Diagram Tabulating and Graphing Bivariate Categorical Data Contingency Tables Side by Side Bar Charts Case Study: Titanic Data Graphical Excellence and Common Errors in Presenting Data (continued)

© 2003 Prentice-Hall, Inc. Guidelines to Analyze data First learn something about the context: What was measured? What are the units? How was the measurement carried out? Where the data measured for a particular purpose? Then make a picture. It is sometimes said that there are three rules for starting a data analysis: Plot the data, plot the data, and plot the data. Look for an overall pattern and for deviations from that pattern. Such deviations are called outliers. 4.1 See a real world problem in which a distribution is needed.

© 2003 Prentice-Hall, Inc. Organizing Numerical Data Numerical Data Ordered Array Stem and Leaf Display Frequency Distributions Cumulative Distributions Histograms Polygons Ogive Tables 41, 24, 32, 26, 27, 27, 30, 24, 38, 21 21, 24, 24, 26, 27, 27, 30, 32, 38, 41

© 2003 Prentice-Hall, Inc. Raw Data in Raw Form (as Collected): 24, 26, 24, 21, 27, 27, 30, 41, 32, 38 Ordered ArraySmallest to Largest Data in Ordered Array from Smallest to Largest: 21, 24, 24, 26, 27, 27, 30, 32, 38, 41 Stem-and-Leaf Display: Organizing Numerical Data (continued)

© 2003 Prentice-Hall, Inc. Tabulating and Graphing Numerical Data Numerical Data Ordered Array Stem and Leaf Display Histograms Ogive Tables 41, 24, 32, 26, 27, 27, 30, 24, 38, 21 21, 24, 24, 26, 27, 27, 30, 32, 38, 41 Frequency Distributions Cumulative Distributions Polygons

© 2003 Prentice-Hall, Inc. Tabulating Numerical Data: Frequency Distributions 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, 58 Find Range: = 46 Select Number of Classes: 5 (usually between 5 and 15) Compute Class Interval (Width): 10 (46/5 then round up) Determine Class Boundaries (Limits): 10, 20, 30, 40, 50, 60 Compute Class Midpoints: 15, 25, 35, 45, 55 Count Observations & Assign to Classes

© 2003 Prentice-Hall, Inc. Frequency Distributions, Relative Frequency Distributions and Percentage Distributions Class Frequency 10 but under but under but under but under but under Total Relative Frequency Percentage Data in Ordered Array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

© 2003 Prentice-Hall, Inc. Graphing Numerical Data: The Histogram Data in Ordered Array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58 No Gaps Between Bars Class Midpoints Class Boundaries

© 2003 Prentice-Hall, Inc. Bar Chart How tall are the tallest soldiers in this group? 1. How many in this group are between 65 and 67 inches tall? 2. If we selected a soldier at random from this group, would you estimate that he or she is more likely to be taller than 65 inches or shorter than 65 inches? (Hint: No calculation is needed. Judge from the way the display looks.)

© 2003 Prentice-Hall, Inc. Graphing Numerical Data: The Frequency Polygon Class Midpoints Data in Ordered Array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

© 2003 Prentice-Hall, Inc. Tabulating Numerical Data: Cumulative Frequency Lower Cumulative Cumulative Limit Frequency % Frequency Data in Ordered Array: 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

© 2003 Prentice-Hall, Inc. Graphing Numerical Data: The Ogive (Cumulative % Polygon) Class Boundaries (Not Midpoints) Data in Ordered Array : 12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43, 44, 46, 53, 58

© 2003 Prentice-Hall, Inc. Graphing Bivariate Numerical Data (Scatter Plot)

© 2003 Prentice-Hall, Inc. Tabulating and Graphing Univariate Categorical Data Categorical Data Tabulating Data The Summary Table Graphing Data Pie Charts Pareto Diagram Bar Charts

© 2003 Prentice-Hall, Inc. Univariate and Bivariate Analysis by Tables and Charts of Car Data Variables: Miles per Gallon Type of Drive Weight

© 2003 Prentice-Hall, Inc. Variables We will be looking at 3 variables relating to cars We Will use Histograms Frequency and Percentage Polygon Ogives Scatter Plots (Bivariate Data)

© 2003 Prentice-Hall, Inc. The following Data Relates to Front and Rear Wheel Drive Cars

© 2003 Prentice-Hall, Inc. Ogive: Front Wheel Drive What percentage of the Front wheel Drive Cars do: - More than 19 miles per gallon Less than 27 Miles per gallon Estimate the miles per gallon for: - 50 Percentile of Front Wheel Drive Cars: 25 Percentile of Front Wheel Drive Cars

© 2003 Prentice-Hall, Inc. Ogive: Rear Wheel Drive What percentage of the Rear wheel Drive Cars do: - More than 19 miles per gallon Less than 27 Miles per gallon Estimate the miles per gallon for: - 50 Percentile of Rear Wheel Drive Cars: Rear Percentile of Front Wheel Drive Cars

© 2003 Prentice-Hall, Inc. To Compare Distributions Compare Frequency and Percentage Polygons for Front and Rear Drive Cars Compare Ogives for Front and Rear Drive Cars

© 2003 Prentice-Hall, Inc. Frequency Polygon: Drive Type and Miles per Gallon Answer the Following True or False. This graph shows: There are more Rear Wheel Cars than Front Wheel Cars No Front Wheel Drive Cars Do more than 25 Miles per gallon There are more Front Wheel Drive Cars that do 21 Miles per gallon than Rear Wheel Drive Cars

© 2003 Prentice-Hall, Inc. Percentage Polygon: Drive Type and Miles per Gallon Answer the Following True or False. This graph shows: Overall the miles per gallon for Rear Wheel is not as good as Front Wheel Drive Cars 40% of Front Wheel Drive Cars do 21 Miles per gallon There are more Front Wheel Drive Cars that do 21 Miles per gallon than Rear Wheel Drive Cars

© 2003 Prentice-Hall, Inc. Cumulative Percentage Polygon: Drive Type and Miles per Gallon Answer the Following True or False. This graph shows: Overall the miles per gallon for Front Wheel is better than Rear Wheel Drive Cars 80% of Front Wheel Drive Cars do less than 21 Miles per gallon

© 2003 Prentice-Hall, Inc. Car Weight (lbs) V’s Miles per Gallon Answer the Following True or False. This graph shows: Overall the Weight of the car is associated with the Miles per gallon The Heavier the car the greater the miles per gallon

© 2003 Prentice-Hall, Inc. Displaying Categorical Data Three Rules of Data Analysis: - Make a picture – It will reveal things you can not see on a table and will help you think clearly Make a picture – Well designed display will show the important features and patterns in your data i.e. missing wrong data or unexpected patterns Make Picture –It is the best way to tell others what about your data.

© 2003 Prentice-Hall, Inc. Frequency Tables 1. What is the most common hair color in this group of children? 2. What is the second most common color? 3. Are the categories given here well-defined? 4. If not, how would you improve them? 5. Does this distribution of hair colors resemble the distribution you see among people in Cambodia? 6. If not, how does it differ? FairRedMediumDarkBlack 27%5.3%39.7%25.8 % 2.2%

© 2003 Prentice-Hall, Inc. Bar Chart 1. What is the most common hair color in this group of children? 2. What is the second most common color? 3. Is there a greater difference between the relative frequencies of Red and Black, or between the relative frequencies of Medium and Dark?

© 2003 Prentice-Hall, Inc. Graphing Univariate Categorical Data Categorical Data Tabulating Data The Summary Table Graphing Data Pie Charts Pareto Diagram Bar Charts

© 2003 Prentice-Hall, Inc. Tabulating and Graphing Bivariate Categorical Data Contingency Tables:

© 2003 Prentice-Hall, Inc. Pie Chart (Analyzing Standard of Living in 4 Communes)

© 2003 Prentice-Hall, Inc. Bivariate Categorical Data (for Standard of Living by Commune) Frequency

© 2003 Prentice-Hall, Inc. Stacked Bar Chart Bivariate Categorical Data Which commune has the highest percentage of Poor

© 2003 Prentice-Hall, Inc. Pareto Diagram Axis for line graph shows cumulative % invested Axis for bar chart shows number in each category

© 2003 Prentice-Hall, Inc. Case Study: Titanic Data Part of a table detailing the Titanic Problem with this table - in fact all tables like this – is that you can not really see what is going on We need to show patterns, relationships, trends and even exceptions What are the variables?

© 2003 Prentice-Hall, Inc. Frequency Tables The Count provides the Frequency of each category. The Variable CLASS has only 4 categories so it is very easy to read The Percentage Provides the Relative Frequency What percentage was not crew ?

© 2003 Prentice-Hall, Inc. Example: Create a Frequency Table SurvivedAgeSexClass DeadAdultMaleThird AliveAdultMaleCrew DeadAdultMaleThird DeadChildMaleCrew DeadAdultMaleCrew AliveChildMaleCrew AliveAdultFemaleFirst DeadAdultMaleThird DeadAdultMaleCrew Example: Create 3 Frequency Tables 1.Survived 2.Age 3.Class

© 2003 Prentice-Hall, Inc. Bar Charts Displays the distribution of a categorical variable, showing the counts for each category next to each other for easy comparison What does this graph tell us? Example: Create 6 bar Charts for data on previous slide. 1.Survived: A Frequency B Percentage 2.Age : A Frequency B Percentage 3.Class : A Frequency B Percentage

© 2003 Prentice-Hall, Inc. Pie Charts Pie Chars show us the whole group of cases as a circle. They slice into pieces whose size is proportional to the fraction of the whole in each category Where are there more crew or Third class passengers? Example: Draw 6 Pie Charts for data on previous slide. 1.Survived: A Frequency B Percentage 2.Age : A Frequency B Percentage 3.Class : A Frequency B Percentage

© 2003 Prentice-Hall, Inc. Bivariate Table (Cross Tabulations) Was there a relationship between the CLASS and the chance of surviving? We need to look at Class and Survival together on a contingency table. Marginal Distribution

© 2003 Prentice-Hall, Inc. Example: Cross Tabulations Create a cross tabulation for: 1. Survived and Age 2. Survived and Sex 3. Age and Sex SurvivedAgeSexClass DeadAdultMaleThird AliveAdultMaleCrew DeadAdultMaleThird DeadChildMaleCrew DeadAdultMaleCrew AliveChildMaleCrew AliveAdultFemaleFirst DeadAdultMaleThird DeadAdultMaleCrew

© 2003 Prentice-Hall, Inc. Row Percentages indicate Chance How can the presentation can be improved?

© 2003 Prentice-Hall, Inc. Conditional Distributions makes it clearer We have redefined the WHO of the study into two groups: Who was ALIVE and Who was DEAD Conditional distributions is when one variable has been selected which satisfies some condition? If % of ROW same it shows the distributions are INDEPENDENT of Class How can the presentation can be improved?

© 2003 Prentice-Hall, Inc. Clustered Bar Chart of comparing percentage of Alive and Dead in Titanic Did the Crew, Third Class, Second Class and First Class have the same Chance of Survival (being Alive or Dead)? Class Each bar as the ”Whole” and divides it proportionally into segments corresponding to the percentage in each group.

© 2003 Prentice-Hall, Inc. Data changed to show an Equal Chance of Survival The Conditional Distributions is based on Category Survival. Note now the % Row are equal This means the chance of being alive and dead is the same in each Class. Thus, Survival is independent of Class Modified

© 2003 Prentice-Hall, Inc. Clustered Bar Chart for Equal Chance of Survival Class

© 2003 Prentice-Hall, Inc. Alternatively, create Conditional Distributions split on Class (By Columns) Modified Data to show equal Chance The Passengers in Category First Class have an equal chance of survival….. … as they do in Second Class… … as they do in Third Class… … as they do in Crew …

© 2003 Prentice-Hall, Inc. Pie Charts are also a good choice when you are primarily interested in percentage What does this show? (See Hidden Slide) The Dead (non survivors) are mostly crew and 3rd class passengers, survivors on the other hand are nearly evenly split across the classes. These Pie Charts use original Titanic Data

© 2003 Prentice-Hall, Inc. Results The Dead are mostly crew and 3rd class passengers, The Survivors (Alive) on the other hand are evenly split across the classes. If the percentage in each class had been the same across the two groups ALIVE and DEAD we would have said survival was INDEPENDENT of class. However, the differences between the two conditional distribution suggest that survival may have been dependent on class In a Contingency table, when one distribution of one variable is the same for all categories of another, we say the variables are INDEPENDENT

© 2003 Prentice-Hall, Inc. Examining Contingency tables STEP- BY-STEP Think Variable – Identify the Variables are report the W’s. be certain that the data are counts and the categories do not overlap Show Mechanics – Make an appropriate display to see whether there is a difference in the relative proportions. Bar Charts may work equally well Tell Interpretation – Discuss the pattern in the tables and display and if you can flag any issues to managers to inform them of any consequences. This is extremely important when conducting research.

© 2003 Prentice-Hall, Inc. Example: Cross Tabulations and Graphs You have created a cross tabulation for: 1. Survived and Age 2. Survived and Sex 3. Age and Sex Workout Row percentages and then display them on a Stacked bar or Pie Chart SurvivedAgeSexClass DeadAdultMaleThird AliveAdultMaleCrew DeadAdultMaleThird DeadChildMaleCrew DeadAdultMaleCrew AliveChildMaleCrew AliveAdultFemaleFirst DeadAdultMaleThird DeadAdultMaleCrew

© 2003 Prentice-Hall, Inc. Principles of Graphical Excellence Well-Designed Presentation of Data that Provides: Substance Statistics Design Communicate Complex Ideas with Clarity, Precision and Efficiency Gives the Largest Number of Ideas in the Most Efficient Manner Almost Always Involves Several Dimensions Telling the Truth about the Data

© 2003 Prentice-Hall, Inc. Errors in Presenting Data Using ‘Chart Junk’ No Relative Basis in Comparing Data between Groups Compressing the Vertical Axis No Zero Point on the Vertical Axis

© 2003 Prentice-Hall, Inc. ‘Chart Junk’ Good Presentation 1960: $ : $ : $ : $3.80 Minimum Wage $ Bad Presentation

© 2003 Prentice-Hall, Inc. No Relative Basis Good Presentation A’s received by students Bad Presentation 0  FRSOJRSR Freq.  10  30 FRSOJRSR % FR = Freshmen, SO = Sophomore, JR = Junior, SR = Senior

© 2003 Prentice-Hall, Inc. Compressing Vertical Axis Good Presentation Quarterly Sales Bad Presentation Q1Q2Q3 Q4 $ Q1Q2 Q3 Q4 $

© 2003 Prentice-Hall, Inc. No Zero Point on Vertical Axis Good Presentation Monthly Sales Bad Presentation J F MAMJ $ JFMAMJ $ Graphing the first six months of sales 36

© 2003 Prentice-Hall, Inc. Chapter Summary Organized Numerical Data The Ordered Array and Stem-Leaf Display Tabulated and Graphed Univariate Numerical Data Frequency Distributions: Tables, Histograms, Polygons Cumulative Distributions: Tables, the Ogive Graphed Bivariate Numerical Data

© 2003 Prentice-Hall, Inc. Chapter Summary Tabulated and Graphed Univariate Categorical Data The Summary Table Bar and Pie Charts, the Pareto Diagram Tabulated and Graphed Bivariate Categorical Data Contingency Tables Side by Side Charts Discussed Graphical Excellence and Common Errors in Presenting Data (continued)