David S. Moore • George P. McCabe
Introduction to the
Practice of Statistics
Fifth Edition
Chapter 1:
Looking at Data—Distributions
Copyright © 2005 by W. H. Freeman and Company
Modifications and Additions by M. Leigh Lunsford, 20052006
Class Website
www.IntroStats.blogspot.com
• Policies and Syllabus doc
• Software
• Homework assignments, test
announcements, lecture slides, etc.
• Continually updated - check it regularly!
Technology Requirements
• MegaStat Plugin for Excel (website)
• Data Sets in Excel Format on CD (CD
accompanying text)
• TI-83
What is Statistics??
The Science of Learning from Data
The Collection and Analysis of Data
Experimental Design
Chapter 3
Probability
Chapter 4
Descriptive Statistics
(Data Exploration)
Chapters 1, 2
Inferential Statistics
Chapters 5 - 8
Chapter 1 - Looking at Data
1.1 Displaying Distributions with Graphs
1.2 Describing Distributions with Numbers
1.3 Density Curves and Normal
Distributions
Section 1.1
Displaying Distributions with
Graphs
Data Basics
Variable Types
An Example (p. 5)
Graphs for Categorical Vars.
• Bar Graphs
• Pie Charts
Educational Level Example (page 7):
– A Bar Graph by Hand
– A Pie Chart by Hand
Homework: Try to do these in Excel!
Graphs for Quantitative Data
• Stemplots (Stem and Leaf Plots)
– Generally for small data sets
• Histograms
• Time Plots (if applicable)
Let’s look at an example to see what types of questions one
may ask and how these plots help to visualize the answers!
Example 1.7 Page 14
Descriptive and Inferential Stats
1.
2.
3.
4.
What percent of the 60 randomly chosen fifth grade
students have an IQ score of at least 120?
Based on this data, approximately what percent of
all fifth grade students have an IQ score of at least
120?
What is the average IQ score of the fifth grade
students in this sample?
Based on this data, what is the average IQ score of
all fifth grade students (i.e. the population) from
which the sample was drawn?
Inferential? 2 and 4
Descriptive? 1 and 3
Let’s Make a Stemplot!
An Example (Ex. 1.7 p.14)
Data in Table 1.3 p. 14 (and on next slide)
Stem and Leaf Plot for Example
IQ Test Scores for 60 Randomly Chosen
5th Grade Students
Generated Using the Descriptive Statistics Menu on Megastat
Stem and Leaf plot for
iq
stem unit =
10
leaf unit =
1
Frequency
Stem
3
8
129
4
9
0467
14
10
01112223568999
17
11
00022334445677788
11
12
22344456778
9
13
013446799
2
14
25
60
Leaf
Now Let’s Make a Histogram!
• Use the Same Data in Example 1.7
(Data in Table 1.3)
• We will start by hand….using class
widths of 10 starting at 80…
• Compare the Stemplot to the
Histogram!
Histogram for Example
iq
lower
cumulative
upper
midpoint
width
frequency
percent
frequency
percent
80
<
90
85
10
3
5.0
3
5.0
90
<
100
95
10
4
6.7
7
11.7
100
<
110
105
10
14
23.3
21
35.0
110
<
120
115
10
17
28.3
38
63.3
120
<
130
125
10
11
18.3
49
81.7
130
<
140
135
10
9
15.0
58
96.7
140
<
150
145
10
2
3.3
60
100.0
60
100.0
IQ Scores of Randomly Chosen Fifth Grade Students
30
25
Compare this
Histogram to the Stem
& Leaf Plot we
Generated Earlier!
15
10
5
IQ Score
15
0
14
0
13
0
12
0
11
0
10
0
90
0
80
Percent
20
Recall Our Earlier Question 1
1. What percent of the 60 randomly
chosen fifth grade students have an IQ
score of at least 120?
• Numerically?
18.3%+15%+3.3%=36.6%
(11+9+2)/60=.367 or 36.7%
• How to Represent
Graphically? Grey Shaded Region corresponds to this
36.6% of data
What is different from the
histogram we generated
in class??
Descriptors we will
be interested in for
data and population
distributions.
Let’s Look at the Distribution we Just Created:
• Overall Pattern:
Shape (modes, tails (skewness), symmetry)
Center (mean, median)
Spread (range, IQR, standard deviation)
• Deviations:
Outliers
• Overall Pattern:
Shape, Center, Spread?
• Deviations:
Outliers?
Data Analysis – An Interesting
Example (p. 9)!
80 Calls
•Overall Pattern:
Shape, Center, Spread?
•Deviations:
Outliers?
Moral of this story:
making your class widths
too small can obscure
important features of your
data.
Time Plots – For Data Collected
Over Time…
Example: Mississippi River
Discharge p.19 (data p. 21)
Example – Dealing with
Seasonal Variation
Original data
Seasonal variation
Trend line
Residuals = original data - trend line - seasonal variation
Extra Slides from Homework
•
•
•
•
•
•
Problem 1.19
Problem 1.20
Problem 1.21
Problem 1.31
Problem 1.36
Problem 1.37-1.38
Problem 1.19, page 30
Problem 1.20, page 31
Problem 1.21, page 31
Problem 1.31, page 36