1. Sections 1.1-1.2 TAKE OUT YOUR NOTES, Book & Do Page 8 #7-8
Chapter 1
Sections
TAKE OUT YOUR NOTES, Book &
Do Page 8 #7-8

2. I. Three Rules of Data Analysis
Make a picture (Rule 1, 2 & 3)
Shows patterns and relationships
Shows extraordinary parts to data
Good for demonstrations

3. Relative Frequency Table
II. Count the number of cases corresponding to each category & pile them up.
III. Frequency table
Records totals
Records category names
Can use counts, proportions or percentages (relative frequency table)
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
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

4. IV. Area Principle V. Bar Graphs (Charts) Remember the iMacs graph
(pictograph at right)
Area occupied by a part of the
graph should correspond to the
magnitude of the value it represents.
V. Bar Graphs (Charts)
Displays distribution of categorical variables.
Used for easy comparison
Has small spaces between bars

5. Analyzing Categorical Data
Graphs: Good and Bad
Bar graphs compare several quantities by comparing the heights of bars that represent those quantities.
Our eyes react to the area of the bars as well as height. Be sure to make your bars equally wide.
Avoid the temptation to replace the bars with pictures for greater appeal…this can be misleading!
Analyzing Categorical Data
Alternate Example: The following ad for DIRECTV has multiple problems. See how many your students can point out. First, the heights of the bars are not accurate. According to the graph, the difference between 81 and 95 is much greater than the difference between 56 and 81. Also, the extra width for the DIRECTV bar is deceptive since our eyes respond to the area, not just the height.
Check for Understanding
This ad for DIRECTV has multiple problems. How many can you point out?

6. VII. Contingency (Two-Way) Tables
VI. Pie Charts
Shows a whole group broken into categories
Cannot be used if overlap between groups.
VII. Contingency (Two-Way) Tables
Displays counts of individuals classified
If convert counts to row percentages, then comparisons can be made.
Contains marginal distributions (frequency distributions in table)

7. VIII. Always ask “Percent of What?” IX. Conditional Distributions
Show one variable for the individuals who satisfy some condition
Normally use row percentages.
X. Independent – when the distribution of one variable is the same for all categories
XI. Segmented Bar Chart – divides a bar into percentages for comparison

8. Analyzing Categorical Data
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.
Analyzing Categorical Data
Definition:
Two-way Table – describes two categorical variables, organizing counts according to a row variable and a column variable.
Alternate Example: Super Powers
A sample of 200 children from the United Kingdom ages 9-17 was selected from the CensusAtSchool website ( The gender of each student was recorded along with which super power they would most like to have: invisibility, super strength, telepathy (ability to read minds), ability to fly, or ability to freeze time. Here are the results:
Example, p. 12
What are the variables described by this two-way table?
How many young adults were surveyed?
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

9. Analyzing Categorical Data
Two-Way Tables and Marginal Distributions
Analyzing Categorical Data
Definition:
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.
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.

10. Analyzing Categorical Data
Two-Way Tables and Marginal Distributions
Analyzing Categorical Data
Example, p. 13
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
Examine the marginal distribution of chance of getting rich.
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%

11. When analyzing a Problem
4 Step Process
State – What are you trying to answer?
Plan – How will you answer the question?
Do – Make graphs and complete calculations
Conclude – Write a conclusion in context

12. CAUTION Partner Check Keep the area principle. Keep it honest.
Look at the variables separately.
Be sure to use enough individuals.
Beware of Simpson’s paradox (averaging across groups)
Partner Check
Page 23 #15

13. Analyzing Categorical Data
Two-Way Tables and Conditional Distributions
Example, p. 15
Analyzing Categorical Data
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
Calculate the conditional distribution of opinion among males.
Examine the relationship between gender and opinion.
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%

14. Segmented Bar Chart
Activity 7-2
Partner Check
Activity 7-8

15. Homework
Pages #10, 20, 22, 26

16. Warm-up
Pages #27-32 all

17. I. IMPORTANT
Always identify the shape, center, spread and unusual features (outliers, gaps, clusters) of the distribution.
Always make a picture.
SOCS

18. II. Shape Unimodal ~ one main peak Bimodal ~ two main peaks
Multimodal ~ three or more peaks
Uniform ~ no apparent peaks
Symmetric ~ can fold graph onto itself
Skewed
One tail is longer than another
Skewed in direction of longer tail
II. Shape

19. III. Bar Graphs are used for categorical data and have breaks between bars, where histograms are used for quantitative data and are continuous. IV. Relative Frequency Histograms use percentages instead of counts.
# of Months
% of Months

20. Displaying Quantitative Data
Making a Histogram
The table on page 35 presents data on the percent of residents from each state who were born outside of the U.S.
Example, page 35
Displaying Quantitative Data
Frequency Table
Class
Count
0 to <5 20
5 to <10 13
10 to <15 9
15 to <20 5
20 to <25 2
25 to <30 1
Total 50
Percent of foreign-born residents
Number of States

21. VI. Stem-and-Leaf (Stemplots)
V. Histograms
Show distribution and spread
Lose individual data
Good for large sets of data
Label the axes
VI. Stem-and-Leaf (Stemplots)
Keeps individual data
Can be turned to see distribution
Should include a key
Dotplots
Good for small data sets
Shows spread

22. Hiring Discrimination
VIII. Outliers and gaps can skew data.
When comparing distributions using graphs, always use the same scale.
Skewed data can be re-expressed in order to transform the graph.
Cautions
Avoid inconsistent scales.
Label clearly
Structured Activity
Hiring Discrimination

23. Pages 43-48
#42, 46, 48, 56, 68
Homework

24. Ticket out the Door
Pages #2-4