Chapter 1
Sections 1.1-1.2
TAKE OUT YOUR NOTES, Book &
Do Page 8 #7-8
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
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
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
Total
1579
13838
Format
Adult Contemporary
Percent of Stations
11.2
Adult Standards
8.6
Contemporary Hit
4.1
Country
14.9
News/Talk
15.7
Oldies
Religious
7.7
14.6
Rock
6.3
Spanish Language
5.4
Other Formats
11.4
Total
99.9
IV. Area Principle


V.
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.
Bar Graphs (Charts)
A.
B.
C.
Displays distribution of categorical
variables.
Used for easy comparison
Has small spaces between bars
 Graphs:
Good and Bad
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!
Check for Understanding
This ad for DIRECTV
has multiple problems.
How many can you
point out?
Analyzing Categorical Data
Bar graphs compare several quantities by comparing
the heights of bars that represent those quantities.
VI. Pie Charts
A.
B.
Shows a whole group broken into
categories
Cannot be used if overlap between groups.
VII. Contingency (Two-Way) Tables
A.
B.
C.
Displays counts of individuals classified
If convert counts to row percentages, then
comparisons can be made.
Contains marginal distributions (frequency
distributions in table)
VIII. Always ask “Percent of What?”
IX. Conditional Distributions
A.
B.
Show one variable for the individuals who
satisfy some condition
Normally use row percentages.
Independent – when the distribution of
one variable is the same for all
categories
XI. Segmented Bar Chart – divides a bar
into percentages for comparison
X.
Definition:
Two-way Table – describes two categorical
variables, organizing counts according to a row
variable and a column variable.
Example, p. 12
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 50-50 chance
696
720
1416
A good chance
663
758
1421
Almost certain
486
597
1083
Total
2367
2459
4826
What are the variables
described by this twoway table?
How many young
adults were surveyed?
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.
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,
1)Use the data in the table to calculate the marginal
distribution (in percents) of the row or column totals.
2)Make a graph to display the marginal distribution.
Analyzing Categorical Data
 Two-Way Tables and Marginal Distributions
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 50-50 chance
696
720
1416
A good chance
663
758
1421
Almost certain
486
597
1083
Total
2367
2459
4826
Chance of being wealthy by age 30
Percent
Almost no chance
194/4826 =
4.0%
Some chance
712/4826 =
14.8%
A 50-50 chance
1416/4826 =
29.3%
A good chance
1421/4826 =
29.4%
Almost certain
1083/4826 =
22.4%
Percent
Response
Examine the marginal
distribution of chance
of getting rich.
35
30
25
20
15
10
5
0
Almost
none
Some
50-50
Good
chance
chance
chance
Survey Response
Almost
certain
Analyzing Categorical Data
 Two-Way Tables and Marginal Distributions
When analyzing a Problem
 4 Step Process
1. State – What are you trying to answer?
2. Plan – How will you answer the
question?
3. Do – Make graphs and complete
calculations
4. Conclude – Write a conclusion in
context
CAUTION





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
 Two-Way Tables and Conditional Distributions
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 50-50 chance
696
720
1416
A good chance
663
758
1421
Almost certain
486
597
1083
Total
2367
2459
4826
Male
Female
Almost no chance
98/2459 =
4.0%
96/2367 =
4.1%
Some chance
286/2459 =
11.6%
426/2367 =
18.0%
A 50-50 chance
720/2459 =
29.3%
696/2367 =
29.4%
758/2459 =
30.8%
663/2367 =
28.0%
597/2459 =
24.3%
486/2367 =
20.5%
A good chance
Almost certain
Chance
by
age
Chanceofofbeing
being wealthy
wealthy
age
3030
Chance
being
wealthyby
by
age
30
Percent
Percent
Percent
Response
Calculate the conditional
distribution of opinion
among males.
Examine the relationship
between gender and
opinion.
100%
90%
80%
70%
35
60%
30
25
50%
20
40%
15
10
30%
5
20%
0
10%Almost
Almost no
Some
no Some
chance
chance
chance
chance
0%
Almost certain
Good chance
Analyzing Categorical Data
Example, p. 15
Males
50-50 chance
Males
50-50
50-50
chance
chance
Good
Good
chance
chance
Males
Females
OpinionOpinion
Opinion
Females
Almost
Almost
Some chance
certain
certain
Almost no chance
Segmented Bar Chart
 Activity 7-2
Partner Check
Activity 7-8
Homework
 Pages 22-24 #10, 20, 22, 26
Warm-up
Pages 25-26 #27-32 all
I. IMPORTANT
Always identify the shape,
center, spread and unusual
features (outliers, gaps,
clusters) of the distribution.
 Always make a picture.

A. Unimodal ~ one main peak
B. Bimodal ~ two main peaks
C. Multimodal ~ three or more
peaks
D. Uniform ~ no apparent peaks
E. Symmetric ~ can fold graph
onto itself
F. Skewed
1. One tail is longer than another
2. Skewed in direction of longer tail
II.Shape
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
Example, page 35
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.
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
Number of States
Frequency Table
Percent of foreign-born residents
Displaying Quantitative Data

V.
Histograms
A.
B.
C.
D.
Show distribution and spread
Lose individual data
Good for large sets of data
Label the axes
VI. Stem-and-Leaf (Stemplots)
A.
B.
C.
Keeps individual data
Can be turned to see distribution
Should include a key
VII. Dotplots
A.
B.
Good for small data sets
Shows spread
VIII. Outliers and gaps can skew data.
IX. When comparing distributions using
graphs, always use the same scale.
X. Skewed data can be re-expressed in
order to transform the graph.
XI. Cautions
A.
B.
Avoid inconsistent scales.
Label clearly
Structured Activity
Hiring Discrimination
 Pages 43-48
◦ #42, 46, 48, 56, 68
Homework
Ticket out the Door
Pages 34-35 #2-4