1. Graphical and Numerical Summaries of Qualitative Data
OBJECTIVES
At the conclusion of this set and the next set of slides you should be able to:
1) Construct graphs that appropriately describe data
2) Calculate and interpret numerical summaries of a data set.
3) Combine numerical methods with graphical methods to analyze a data set.

2. Displaying Qualitative Data
“Sometimes you can see a lot just by looking.”
Yogi Berra
Hall of Fame Catcher, NY Yankees
Beginning of lecture unit 2 in coursepack

3. The three rules of data analysis won’t be difficult to remember
1. Make a picture —reveals aspects not obvious in the raw data; enables you to think clearly about the patterns and relationships that may be hiding in your data.
2. Make a picture —to show important features of and patterns in the data. You may also see things that you did not expect: the extraordinary (possibly wrong) data values or unexpected patterns
3. Make a picture —the best way to tell others about your data is with a well-chosen picture.

4. Bar Charts: show counts or relative frequency for each category
Example: Titanic passenger/crew distribution
Page 2 lecture unit 2

5. Pie Charts: shows proportions of the whole in each category
Example: Titanic passenger/crew distribution
Page 2 lecture unit 2

6. Example: Recent annual top 10 causes of death in the United States
Rank
Causes of death
Counts
% of top 10s
% of total deaths 1
Heart disease
700,142
37%
28% 2
Cancer
553,768
29%
22% 3
Cerebrovascular
163,538 9% 6% 4
Chronic respiratory
123,013 5% 5
Accidents
101,537 4% 6
Diabetes mellitus
71,372 3% 7
Flu and pneumonia
62,034 2% 8
Alzheimer’s disease
53,852 9
Kidney disorders
39,480 10
Septicemia
32,238 1%
All other causes
629,967
25%
For each individual who died in the United States, we record what was the cause of death. The table above is a summary of that information.

7. Top 10 causes of death: bar graph
Each category is represented by one bar. The bar’s height shows the count (or sometimes the percentage) for that particular category.
Top 10 causes of deaths in the United States
The number of individuals who died of an accident is approximately 100,000.

8. Top 10 causes of deaths in the United States
Bar graph sorted by rank
 Easy to analyze
Sorted alphabetically
 Much less useful

9. Top 10 causes of death: pie chart
Each slice represents a piece of one whole. The size of a slice depends on what
percent of the whole this category represents.
Percent of people dying from
top 10 causes of death in the United States
Another way to graphically illustrate the same categorical data is using a Pie Chart.
Here is listed in order, and can see relative proportions as pieces of pie.
Notice here that we have changed from the numbers of people dying to the percent of people dying
To make a pie chart, typically use percentages, and they have to add up to one, or you won’t have the whole pie. ?

10. Make sure your labels match the data. Make sure all percents
add up to 100.
Percent of deaths from top 10 causes
The top pie chart is the one we have just been looking at.
In the bottom one I have added deaths from all other causes - 21% in addition to the top 10. Adding this additional category changes the percentages on the original 10, so, for instance
Heart disease was 37% of total before, now is a smaller percent, 29%, because we are looking at
All deaths.
Percent of deaths from all causes

13. Side-by side bar chart

14. Student Debt North Carolina Schools

15. Contingency Tables: Categories for Two Variables
Example: Survival and class on the Titanic
Marginal distributions
marg. dist. of survival
710/ %
1491/ %
Pages 2/3 of lecture unit 2 coursepack
marg. dist. of class
885/ %
325/ %
285/ %
706/ %

16. Marginal distribution of class. Bar chart.

17. Marginal distribution of class: Pie chart

18. Contingency Tables: Categories for Two Variables (cont.)
Conditional distributions.
Given the class of a passenger, what is the chance the passenger survived?
Top p. 3 lecture unit 2 coursepack

19. Conditional distributions: segmented bar chart

20. Contingency Tables: Categories for Two Variables (cont.)
Questions:
What fraction of survivors were in first class?
What fraction of all passengers were in first class and survivors ?
What fraction of the first class passengers survived?
202/710
202/2201
202/325
Top p. 3 lecture unit 2 coursepack

21. TV viewers during recent Super Bowl
TV viewers during recent Super Bowl. What is the marginal distribution of those who watched the commercials only?
8.0%
23.5%
58.2%
27.7%

22. TV viewers during recent Super Bowl
TV viewers during recent Super Bowl. What percentage watched the Game and were Female?
41.8%
38.8%
51.2%
19.8%

23. TV viewers during recent Super Bowl
TV viewers during recent Super Bowl. Given that a viewer did not watch the Super Bowl Game or Commercials, what percentage were male?
45.2%
48.8%
26.8%
27.7%

24. 3-Way Tables Example: Georgia death-sentence data
Page 3 lecture unit 2 coursepack

25. UC Berkeley Lawsuit Lawsuit from 1970’s to show Simpson’s paradox
Higher percentage of men applicants admitted resulted in lawsuit against university

26. LAWSUIT (cont.) Women have higher admission rates in 4 of 6 majors
What gives?
Explanation at top of p. 4 lecture unit 2 coursepack

27. Simpson’s Paradox
The reversal of the direction of a comparison or association when data from several groups are combined to form a single group.

28. Fly Alaska Airlines, the on-time airline!
As a result of the above newspaper ad by Alaska Airlines, American West is losing customers.
You are a highly-paid, famous business consultant and American West calls you for help. They want to know what to do to get their customers back.
What should they do? Nothing.

29. American West Wins! You’re a Hero!
Calculation of overall percentages shown in middle of p. 4 lecture unit 2.

30. TA-DAAAA! The End