1. CHAPTER 1 Exploring Data
Introduction
Data Analysis:
Making Sense of Data

2. Data Analysis: Making Sense of Data
IDENTIFY the individuals and variables in a set of data
CLASSIFY variables as categorical or quantitative
DEFINE “Distribution”
DESCRIBE the idea behind “Inference”

3. Data Analysis
Statistics is the science of data. Data Analysis is the process of organizing, displaying, summarizing, and asking questions about data.
Individuals
objects described by a set of data
Variable
any characteristic of an individual
Categorical Variable
places an individual into one of several groups or categories.
Quantitative Variable
takes numerical values for which it makes sense to find an average.

4. Example: Quantitative or Categorical?
Class (fr, soph, jun, sen) Grade point average address Name Bus route Phone number Days absent

5. Example: Quantitative or Categorical?
Address
Number of Credits earned
Allergies
Exterior color
Mileage
Total car length
Number of cylinders

6. Example: Quantitative or Categorical?
Cost
Model
VIN
Type of sound system
Size of fuel tank
Zip code
Shoe Size

7. Dotplot of MPG Distribution
Data Analysis
A variable generally takes on many different values.
We are interested in how often a variable takes on each value.
Distribution
tells us what values a variable takes and how often it takes those values.
Dotplot of MPG Distribution
Variable of Interest:
MPG

8. Example

9. How to Explore Data Examine each variable by itself.
Then study relationships among the variables.
Start with a graph
or graphs
Add numerical summaries

10. From Data Analysis to Inference
Population
Sample
Collect data from a representative Sample...
Make an Inference about the Population.
Perform Data Analysis, keeping probability in mind…

11. Data Analysis: Making Sense of Data
A dataset contains information on individuals.
For each individual, data give values for one or more variables.
Variables can be categorical or quantitative.
The distribution of a variable describes what values it takes and how often it takes them.
Inference is the process of making a conclusion about a population based on a sample set of data.

12. CHAPTER 1 Exploring Data
1.1 Analyzing Categorical Data

13. Analyzing Categorical Data
DISPLAY categorical data with a bar graph
IDENTIFY what makes some graphs of categorical data deceptive
CALCULATE and DISPLAY the marginal distribution of a categorical variable from a two-way table
CALCULATE and DISPLAY the conditional distribution of a categorical variable for a particular value of the other categorical variable in a two-way table
DESCRIBE the association between two categorical variables

14. Categorical Variables
Categorical variables place individuals into one of several groups or categories.
Frequency Table
Format
Count of Stations
Adult Contemporary
1556
Adult Standards
1196
Contemporary Hit
569
Country
2066
News/Talk
2179
Oldies
1060
Religious
2014
Rock
869
Spanish Language
750
Other Formats
1579
Total
13838
Relative Frequency Table
Format
Percent of Stations
Adult Contemporary
11.2
Adult Standards
8.6
Contemporary Hit
4.1
Country
14.9
News/Talk
15.7
Oldies
7.7
Religious
14.6
Rock
6.3
Spanish Language
5.4
Other Formats
11.4
Total
99.9
Variable
Count
Percent
Values

15. Displaying Categorical Data
Frequency tables can be difficult to read. Sometimes it is easier to analyze a distribution by displaying it with a bar graph or pie chart.
Frequency Table
Format
Count of Stations
Adult Contemporary
1556
Adult Standards
1196
Contemporary Hit
569
Country
2066
News/Talk
2179
Oldies
1060
Religious
2014
Rock
869
Spanish Language
750
Other Formats
1579
Total
13838
Relative Frequency Table
Format
Percent of Stations
Adult Contemporary
11.2
Adult Standards
8.6
Contemporary Hit
4.1
Country
14.9
News/Talk
15.7
Oldies
7.7
Religious
14.6
Rock
6.3
Spanish Language
5.4
Other Formats
11.4
Total
99.9

16. Bar Graphs and Pie Charts
Each bar must be same width.
Can display as count or percentage
Scale should start at 0
Pie Charts
Need to know the percentages to create.
Must add up to 100% (must be parts of a whole)
Can add another category when appropriate so that percentages total 100%.
Use when you want to emphasize each category’s relation to the whole.

17. Graphs: Good and Bad
Bar graphs compare several quantities by comparing the heights of bars that represent those quantities. Our eyes, however, react to the area of the bars as well as to their height.
When you draw a bar graph, make the bars equally wide.
It is tempting to replace the bars with pictures for greater eye appeal.
Don’t do it!
There are two important lessons to keep in mind:
beware the pictograph, and
watch those scales.

18. Graphs: Good and Bad

19. Graphs: Good and Bad
This ad for DIRECTV has multiple problems. How many can you point out?

20. Graphs: Good and Bad

22. Careful with Scales!

23. These graphs show the same information: Google: 30% Yahoo: 35% MSN: 35%

25. Most Deceptive Graph Award

26. Homework
pg. 6-7 # 1, 3, 5, 7, 8 pg #11, 13, 15, 17

27. Chapter 1: Exploring Data
Section 1.1: Analyzing Categorical Data

28. Recap

29. Two-Way Tables and Marginal Distributions
When a dataset involves two categorical variables, we begin by examining the counts or percents in various categories for one of the variables.
A two-way table describes two categorical variables, organizing counts according to a row variable and a column variable.
Young adults by gender and chance of getting rich
Female
Male
Total
Almost no chance 96 98
194
Some chance, but probably not
426
286
712
A chance
696
720
1416
A good chance
663
758
1421
Almost certain
486
597
1083
2367
2459
4826
What are the variables described by this
two-way table?
How many young adults were surveyed?

30. Two-Way Tables and Marginal Distributions
The marginal distribution of one of the categorical variables in a two-way table of counts is the distribution of values of that variable among all individuals described by the table.
Note: Percents are often more informative than counts, especially when comparing groups of different sizes.
How to examine a marginal distribution:
Use the data in the table to calculate the marginal distribution (in percents) of the row or column totals.
Make a graph to display the marginal distribution.

31. Two-Way Tables and Marginal Distributions
Examine the marginal distribution of chance of getting rich.
Young adults by gender and chance of getting rich
Female
Male
Total
Almost no chance 96 98
194
Some chance, but probably not
426
286
712
A chance
696
720
1416
A good chance
663
758
1421
Almost certain
486
597
1083
2367
2459
4826
Response
Percent
Almost no chance
194/4826 = 4.0%
Some chance
712/4826 = 14.8%
A chance
1416/4826 = 29.3%
A good chance
1421/4826 = 29.4%
Almost certain
1083/4826 = 22.4%

32. Homework
Pg. 22 #19, 20

33. Relationships Between Categorical Variables
A conditional distribution of a variable describes the values of that variable among individuals who have a specific value of another variable.
How to examine or compare conditional distributions:
Select the row(s) or column(s) of interest.
Use the data in the table to calculate the conditional distribution (in percents) of the row(s) or column(s).
Make a graph to display the conditional distribution.
Use a side-by-side bar graph or segmented bar graph to compare distributions.

34. Relationships Between Categorical Variables
Calculate the conditional distribution of opinion among males and then females. Examine the relationship between gender and opinion.
Young adults by gender and chance of getting rich
Female
Male
Total
Almost no chance 96 98
194
Some chance, but probably not
426
286
712
A chance
696
720
1416
A good chance
663
758
1421
Almost certain
486
597
1083
2367
2459
4826
Response
Male
Almost no chance
98/2459 = 4.0%
Some chance
286/2459 = 11.6%
A chance
720/2459 = 29.3%
A good chance
758/2459 = 30.8%
Almost certain
597/2459 = 24.3%
Female
96/2367 = 4.1%
426/2367 = 18.0%
696/2367 = 29.4%
663/2367 = 28.0%
486/2367 = 20.5%

35. Conclusion
What does this tell us about the relationship between gender and opinion about future wealth for this sample of young adults? -There does seem to be an association between the two variables for this sample. -Men more often rated their chances in the two highest categories, while women said “some chance” much more frequently than men.

36. Relationships Between Categorical Variables
Can we say there is an association between gender and opinion in the population of young adults? Making this determination requires formal inference, which will have to wait a few chapters.
Caution!
Even a strong association between two categorical variables can be influenced by other variables lurking in the background.

37. Superpowers
A sample of 200 children from the United Kingdom aged 9-17 was selected from the CensusAtSchool Web site. The gender of each student was recorded along with which superpower they would most like to have: invisibility, superstrength, telepathy, ability to fly, ability to freeze time. Here are the results:

38. Superpowers
1. Use the data in the two-way table to calculate the marginal distribution (in percents) of superpower preferences. 2. Make a graph to display the marginal distribution. Describe what you see. 3. Do these data suggest that there is an association between gender and superpower preference? Give appropriate evidence to support your answer.

39. Data Analysis: Making Sense of Data
DISPLAY categorical data with a bar graph
IDENTIFY what makes some graphs of categorical data deceptive
CALCULATE and DISPLAY the marginal distribution of a categorical variable from a two-way table
CALCULATE and DISPLAY the conditional distribution of a categorical variable for a particular value of the other categorical variable in a two-way table
DESCRIBE the association between two categorical variables

40. Homework
pg #21, 23, 26, 27-34