Warm Up
Who talks more—men or women? According to the
author of The Female Brain, women say nearly three times as
many words per day as men. Skeptical researchers devised a study
to test this claim. They used electronic devices to record the
talking patterns of 396 university students from Texas, Arizona,
and Mexico. The device was programmed to record 30 seconds of
sound every 12.5 minutes without the carrier’s knowledge. What
were the results? According to a published report, “Men showed a
slightly wider variability in words uttered….But in the end, the
sexes came out just about even in the daily averages: women at
16,215 words and men at 15,669.”
(a) Did researchers conduct an observational study or an
experiment? Explain.
(b) Why was it important for the recording device to operate
without the knowledge of the carrier?
(c) To what population can the results of this study be
generalized? Justify your answer.
Lesson 3: Organization of Data
Table 2.1
Level of Education of People 25 to 34 Years Old in the
United States, 2007
From Statistics Through Application pg. 37
Displaying Distributions within a Table
Table 2.1
Classes:
Counts:
Rates:
Distribution:
Level of Education of People 25 to 34 Years Old in the
United States, 2007
From Statistics Through Application pg. 37
Consistency
Round off errors:
Table 2.1
Level of Education of People 25 to 34 Years Old in the
United States, 2007
From Statistics Through Application pg. 37
Bar Graphs
A bar graph (or bar chart) is a graphical display of data
using bars of different heights.
Lets say you took a survey of your friends to find out
which kind of movie they liked best. The results of the
survey would look like this in a table.
Favorite Type of Movie
Comedy
Action
Romance
Drama
SciFi
4
5
6
1
4
Bar Graphs
Bar Graphs
Table 2.1
Figure 2.1
Level of Education of People 25 to 34 Years
Old in the United States, 2007
From Statistics Through Application pg. 37
Bar graph of the distribution of level of
education for persons aged 25 to 34 in
the United States in 2007.
From Statistics Through Application pg.
38
Constructing a Bar Graph
Average cost per mile for passenger
vehicles on state turnpikes
STATE
COST
Indiana
2.9¢
Oklahoma
4.3¢
Florida
6.0¢
Maine
3.8¢
Pennsylvania
5.8¢
Constructing a Bar Graph
Step 1:
Draw and label the x- and y-axes
6¢
COST
5¢
4¢
Y-Axis
3¢
2¢
X-Axis
1¢
STATES
Constructing a Bar Graph
Step 2:
Draw the bars to the frequencies. Add a title.
6¢
Average cost per mile for passenger
vehicles on state turnpikes
COST
5¢
4¢
3¢
2¢
1¢
STATES
Try one on your own:
Causes for Late Arrival
Number of Occasions
Family Problems
8
Woke Up Late
20
Had to Take the Bus
4
Traffic tie-up
32
Sick
6
Bad Weather
3
Different Reasons Why
People Were Late to Work
35
30
FREQUENCY
25
20
15
10
5
REASONS
Pareto Chart
A type of bar graph displaying categorical
variables, in which the frequencies are
arranged in order from highest to lowest
Savings for the Softball Team
Name
Money Saved
Sue
$53
Allen
$75
Kirk
$47
Steve
$24
Grace
$66
Constructing a Pareto Chart
Step 1:
Rewrite and arrange the data from largest
to smallest according to frequency.
Name
Allen
Grace
Sue
Kirk
Steve
Money Saved
$75
$66
$53
$47
$24
Constructing a Pareto Chart
Step 2:
Construct and label the x- and y-axes.
$80
Money Saved
$70
$60
Y-Axis
$50
$40
$30
X-Axis
$20
$10
Name
Constructing a Pareto Chart
Step 3:
Draw the bars to the frequencies. Add title.
Savings for the Softball Team
$80
Money Saved
$70
$60
$50
$40
$30
$20
$10
Name
Try One on Your Own
Construct a Pareto Chart for the following data:
Kyle has a bag of marbles with 7 green, 8 brown,
4 purple, 6 orange, and 13 red.
Number of Marbles
Kyle’s Marbles
14
12
10
8
6
4
2
Colors
Dot Plots
In a Dot Plot, a set of data is represented by using
dots over a number line. It is the simplest graph for
displaying the distribution of a quantitative variable.
The frequency of the variables is represented by the
dots.
Ages of Oscar Winners
Gender:
Height:
M
45
M
59
M
45
M
42
M
35
Gender:
Height:
Gender:
Height:
F
39
M
46
F
33
M
28
F
25
M
42
F
24
M
36
F
32
M
35
Gender:
Height:
F
32
F
34
F
27
F
30
F
30
Constructing a Dot Plot
Step 1:
Draw a horizontal line and mark it with a
measurement scale (frequency range) that
extends at least as low as the smallest value in
the data set and as high as the largest value in
the data set. Label the frequency range.
20
25
30
35
40
Ages
45
50
55
60
Constructing a Dot Plot
Step 2:
For each observation in the data set, locate the
value on the measurement scale and represent
it by a dot. If two or more observations have the
same value, stack the dots vertically. Add title.
Ages of Oscar Winners
20
25
30
35
40
Ages
45
50
55
60
Constructing Parallel Dot Plots
It may be helpful to compare the distributions of female- and
male-member ages. An effective way of doing this is to
construct parallel dot plots.
Female
Male
20
25
30
35
40
45
50
55
60
20
25
30
35
40
45
50
55
60
Here, parallel lines are drawn for each gender.
The same scale is used for both lines, and the lines are
labeled.
Parallel Dot Plots
Is there a difference in the ages of the Oscar winners who
were male and female?
Comment on the similarities and differences that can be
observed in the dot plot.
Female
20
Male
20
25
25
30
30
35
35
40
40
45
45
50
50
55
55
60
60
Try One on Your Own- Create a Dot Plot
Table 2.3 Highway Gas Mileages for Model Year 2009
Midsize Cars
Figure 2.4
Answer
Minitab
dotplot of EPA highway gas mileage ratings for 24
.
model year 2009 midsize cars
Key Concept
The purpose of a graph is to help us understand
the data.
Ask, “What do I see?”
Key Concept
Look for patterns and deviations.
Key Concept
An outlier in any graph of data is an individual
observation that falls outside the overall pattern
of the graph. An outlier is clearly separated
from the main body of observations.
Many outliers are due to mistakes.
Key Concept
Does it surprise you that the Bentley and RollsRoyce midsize cars have much lower gas
mileages than the other models?
Bentley
Arnage
Rolls-Royce
Phantom
Homework
Chapter 1: (Monday’s lesson)
•
•
•
Read pgs. 18-26
On page 22 problems: 1.25, 1.26, 1.29
On page 26 problems:1.31, 1.32, 1.33
Chapter 2:
•
On pages 40 and 46 problems: 1.25,
1.26, 1.29, 1.31, 1.32, 1.33, 2.1, 2.2,
2.3, 2.4(b-c), 2.5(b), 2.7, 2.9, 2.10