Basic Practice of Statistics - 3rd Edition
 Question: What is the average height of students in this class?
 Answer: Easy, ask everyone the height, and then find the
Chapter 1
average (mean).
 Question: What is the average height of students in
Picturing Distributions with Graphs
University of Utah?
 Answer: Seems complicated. Too many people, it will be
difficult to ask everyone. Ask a sufficiently large number of
people (but still small compared to the total size of students)
and make an estimate using tools from STATISTICS.
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Statistics
 1. How do we select the people to ask? How many people
should we ask?
 2. How do we make an estimate ?
 3. Our estimate will be probably be a little different from the
true value. Can we say how close it is to the true value?
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Chapter 1
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Statistics is a science that involves the extraction of
information from numerical data obtained during an
experiment or from a sample. It involves the design
of the experiment or sampling procedure, the
collection and analysis of the data, and making
inferences (statements) about the population based
upon information in a sample.
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Basic Practice of Statistics - 3rd Edition
Individuals and Variables
name
major
megan
ryan
jacob
antony
ali
guillermo
hao
nicos
susan
bs
egr
ba
bs
egr
bs
bs
ba
ba
score
 Individuals
gpa
25
35
40
50
22
24
31
35
24
 the objects described by a set of data
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2.5
3.5
2.5
2.6
2.3
3.4
3.3
2.9
 may be people, animals, or things
 Variable
 any characteristic of an individual
 can take different values for different individuals
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Variables
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Case Study
The Effect of Hypnosis
on the
Immune System
 Places an individual into one of several groups or categories
 Takes numerical values for which arithmetic operations such as
adding and averaging make sense
reported in Science News, Sept. 4, 1993, p. 153
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Basic Practice of Statistics - 3rd Edition
Case Study
Case Study
 65 college students.
The Effect of Hypnosis
on the
Immune System
 33 easily hypnotized
 32 not easily hypnotized
 white blood cell counts measured
Objective:
To determine if hypnosis strengthens the
disease-fighting capacity of immune cells.
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Case Study
Case Study
 Students randomly assigned to one of three conditions
 white blood cell counts re-measured after one week
 subjects hypnotized, given mental exercise
group
 control group (no treatment)
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 the two white blood cell counts are compared for each
 subjects relaxed in sensory deprivation tank
Chapter 1
 all students viewed a brief video about the immune system.
 results
 hypnotized group showed larger jump in white blood cells
 “easily hypnotized” group showed largest immune enhancement
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Basic Practice of Statistics - 3rd Edition
Case Study
Case Study
Variables measured
Weight Gain Spells
Heart Risk for Women
quantitative
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“Weight, weight change, and coronary heart disease
in women.” W.C. Willett, et. al., vol. 273(6), Journal
of the American Medical Association, Feb. 8, 1995.
 Pre-study white blood cell count
 Post-study white blood cell count
(Reported in Science News, Feb. 4, 1995, p. 108)
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Case Study
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Case Study
 Study started in 1976 with 115,818 women aged 30 to 55
years and without a history of previous CHD.
Weight Gain Spells
Heart Risk for Women
Objective:
To recommend a range of body mass index
(a function of weight and height) in terms of
coronary heart disease (CHD) risk in women.
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 Each woman’s weight (body mass) was determined.
 Each woman was asked her weight at age 18.
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Basic Practice of Statistics - 3rd Edition
Case Study
Case Study
Variables measured
 The cohort of women were followed for 14 years.
 The number of CHD (fatal and nonfatal) cases were counted
(1292 cases).
categorical
 Incidence of coronary heart disease
 Smoker or nonsmoker
 Family history of heart disease
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Distribution
Displaying Distributions
 Tells what values a variable takes and how often it takes these
 Categorical variables
values
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 Pie charts
 Bar graphs
 Can be a table, graph, or function
 Quantitative variables
 Histograms
 Stemplots (stem-and-leaf plots)
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Basic Practice of Statistics - 3rd Edition
Class Make-up on First Day
Class Make-up on First Day
Data Table
Pie Chart
Year
Count
Percent
Freshman
18
41.9%
Sophomore
10
23.3%
Junior
6
14.0%
Senior
9
20.9%
Total
43
100.1%
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Class Make-up on First Day
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Example: U.S. Solid Waste (2000)
Data Table
Bar Graph
Material
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Weight (million tons)
Percent of total
Food scraps
25.9
11.2 %
Glass
12.8
5.5 %
Metals
18.0
7.8 %
Paper, paperboard
86.7
37.4 %
Plastics
24.7
10.7 %
Rubber, leather, textiles
15.8
6.8 %
Wood
12.7
5.5 %
Yard trimmings
27.7
11.9 %
Other
7.5
3.2 %
Total
231.9
100.0 %
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Basic Practice of Statistics - 3rd Edition
Example: U.S. Solid Waste (2000)
Example: U.S. Solid Waste (2000)
Pie Chart
Bar Graph
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Histograms
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Histograms: Class Intervals
 For quantitative variables that take many values
 Divide the possible values into
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(we will only
consider equal widths)
 How many intervals?
 One rule is to calculate the square root of the sample size, and
round up.
 Count how many observations fall in each interval (may
change to percents)
 Size of intervals?
 Draw picture representing distribution
 Divide range of data (max-min) by number of intervals desired,
and round to convenient number
 Pick intervals so each observation can only fall in exactly
one interval (no overlap)
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Basic Practice of Statistics - 3rd Edition
Case Study
Weight Data
Weight Data
Introductory Statistics class
Spring, 1997
Virginia Commonwealth University
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Weight Data: Frequency Table
Count
100 - <120
7
120 - <140
12
140 - <160
7
160 - <180
8
180 - <200
12
200 - <220
4
220 - <240
1
240 -<260
0
260 -<280
sqrt(53) = 7.2,
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Chapter 1
Weight Data: Histogram
Number of students
Weight Group
30
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100 120 140
1
; range (260-100=160) / 8 =
Chapter 1
160 180 200
Weight
220 240
260
280
* Left endpoint is included in the group, right endpoint is not.
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Basic Practice of Statistics - 3rd Edition
Examining the Distribution of
Quantitative Data
Shape of the Data
 Symmetric
 bell shaped
 Overall pattern of graph
 other symmetric shapes
 Deviations from overall pattern
 Asymmetric
 Shape of the data
 right skewed
 Center of the data
 left skewed
 Spread of the data (Variation)
 Unimodal, bimodal
 Outliers
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Symmetric
Bell-Shaped
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Symmetric
Mound-Shaped
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Basic Practice of Statistics - 3rd Edition
Symmetric
Uniform
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Asymmetric
Skewed to the Left
Chapter 1
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Asymmetric
Skewed to the Right
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Outliers
 Extreme values that fall outside the overall pattern
 May occur naturally
 May occur due to error in recording
 May occur due to error in measuring
 Observational unit may be fundamentally different
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Chapter 1
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Basic Practice of Statistics - 3rd Edition
Stemplots
(Stem-and-Leaf Plots)
 For quantitative variables
 Separate each observation into a
(first part of the
number) and a
(the remaining part of the number)
 Write the stems in a vertical column; draw a vertical line
to the right of the stems
 Write each leaf in the row to the right of its stem; order
leaves if desired
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Weight Data:
Stemplot
(Stem & Leaf Plot)
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Chapter 1
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10
11
12
13 5
14
15 2
16
17
18
19 2
20
21
22
23
24
25
26
192
152
135
43
1
2
Weight Data
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Weight Data:
Stemplot
(Stem & Leaf Plot)
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11
12
13
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15
16
17
18
19
20
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22
23
24
25
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0166
009
0034578
00359
08
00257
555
000255
000055567
245
3
025
0
0
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Basic Practice of Statistics - 3rd Edition
Extended Stem-and-Leaf Plots
Extended Stem-and-Leaf Plots
: if all of the data values were between 150 and 179,
then we may choose to use the following stems:
If there are very few stems (when the data cover only a
very small range of values), then we may want to create
more stems by splitting the original stems.
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15
16
16
17
17
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Leaves 0-4 would go on each
upper stem (first “15”), and leaves
5-9 would go on each lower stem
(second “15”).
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Class Make-up on First Day
Time Plots
(Fall Semesters: 1985-1993)
 A time plot shows behavior over time.
 Time is always on the horizontal axis, and the variable being
measured is on the vertical axis.
 Look for an overall pattern (trend), and deviations from this
trend. Connecting the data points by lines may emphasize
this trend.
 Look for patterns that repeat at known regular intervals
(seasonal variations).
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Basic Practice of Statistics - 3rd Edition
Average Tuition (Public vs. Private)
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