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“Statistics are Everywhere” (Note: Please respond to one  of the following two  bulleted items)Find a chart or graph covered in Chapter 2 in an online resource and describe the type of data as well as the type of graphical display used to display the data. Please explain if the graphical display correctly shows the data or could another type of graphical display be used to “visualize” the data better. H.G. Wells once said “Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write!” Take a position on whether you agree or disagree with this statement, and provide a rationale for your response.Chapter 1
The Nature of Probability
and Statistics
Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
1
The Nature of Probability and
Statistics
CHAPTER
Outline
1-1
1-2
1-3
1-4
1-5
1-6
Descriptive and Inferential Statistics
Variables and Types of Data
Data Collection and Sampling Techniques
Observational and Experimental Studies
Uses and Misuses of Statistics
Computers and Calculators
1
The Nature of Probability and
Statistics
Objectives
1
2
3
4
5
6
7
CHAPTER
1
Demonstrate knowledge of statistical terms.
Differentiate between the two branches of statistics.
Identify types of data.
Identify the measurement level for each variable.
Identify the four basic sampling techniques.
Explain the difference between an observational and
an experimental study.
Explain how statistics can be used and misused.
The Nature of Probability and
Statistics
Objectives
8
CHAPTER
1
Explain the importance of computers and calculators
in statistics.
Introduction

Statistics is the science of conducting
studies to
collect,
organize,
summarize,
analyze, and
draw conclusions from data.
Bluman Chapter 1
5
1-1 Descriptive and Inferential
Statistics

A variable is a characteristic or attribute
that can assume different values.

The values that a variable can assume
are called data.

A population consists of all subjects
(human or otherwise) that are studied.

A sample is a subset of the population.
Bluman Chapter 1
6
1-1 Descriptive and Inferential
Statistics

Descriptive statistics consists of the
collection, organization, summarization,
and presentation of data.

Inferential statistics consists of
generalizing from samples to populations,
performing estimations and hypothesis
tests, determining relationships among
variables, and making predictions.
Bluman Chapter 1
7
1-2 Variables and Types of Data
Data
Qualitative
Categorical
Quantitative
Numerical,
Can be ranked
Discrete
Continuous
Countable
5, 29, 8000, etc.
Can be decimals
2.59, 312.1, etc.
Bluman Chapter 1
8
1-2 Recorded Values and
Boundaries
Variable
Length
Recorded Value
15 centimeters
(cm)
Temperature 86 Fahrenheit
(F)
Time
0.43 second
(sec)
Mass
1.6 grams (g)
Bluman Chapter 1
Boundaries
14.5-15.5 cm
85.5-86.5 F
0.425-0.435
sec
1.55-1.65 g
9
1-2 Variables and Types of Data
Levels of Measurement
1.
Nominal – categorical (names)
2.
Ordinal – nominal, plus can be ranked (order)
3.
Interval – ordinal, plus intervals are consistent
4.
Ratio – interval, plus ratios are consistent,
true zero
Bluman Chapter 1
10
1-2 Variables and Types of Data
Determine the measurement level.
Variable
Nominal Ordinal Interval
Ratio Level
Hair Color
Yes
No
Nominal
Zip Code
Yes
No
Nominal
Yes
Yes
No
ACT Score
Yes
Yes
Yes
No
Interval
Height
Yes
Yes
Yes
Yes
Ratio
Age
Yes
Yes
Yes
Yes
Ratio
Temperature (F)
Yes
Yes
Yes
No
Interval
Bluman Chapter 1
Ordinal
11
1-3 Data Collection and Sampling
Techniques
Some Sampling Techniques

Random – random number generator

Systematic – every kth subject

Stratified – divide population into “layers”

Cluster – use intact groups

Convenient – mall surveys
Bluman Chapter 1
12
1-4 Observational and
Experimental Studies

In an observational study, the researcher
merely observes and tries to draw conclusions
based on the observations.
The researcher manipulates the independent
(explanatory) variable and tries to determine
how the manipulation influences the dependent
(outcome) variable in an experimental study.
A confounding variable influences the
dependent variable but cannot be separated
from the independent variable.
Bluman Chapter 1
13
1-5 Uses and Misuses of Statistics

Suspect Samples
 Is
the sample large enough?
 How
was the sample selected?
 Is
the sample representative of the
population?

Ambiguous Averages
 What
particular measure of average was
used and why?
Bluman Chapter 1
14
1-5 Uses and Misuses of Statistics

Changing the Subject
 Are
different values used to represent the
same data?

Detached Statistics
 One

third fewer calories…….than what?
Implied Connections
 Studies
suggest that some people may
understand what this statement means.
Bluman Chapter 1
15
1-5 Uses and Misuses of Statistics

 Are
the scales for the x-axis and y-axis
appropriate for the data?

Faulty Survey Questions
 Do
you feel that statistics teachers should
be paid higher salaries?
 Do
you favor increasing tuition so that
colleges can pay statistics teachers higher
salaries?
Bluman Chapter 1
16
1-6 Computers and Calculators

Microsoft Excel

Microsoft Excel with MegaStat

TI-83/84

Minitab

SAS

SPSS
Bluman Chapter 1
17
Chapter 2
Frequency Distributions
and Graphs
Copyright © 2013 The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
1
CHAPTER
Frequency Distributions and Graphs
Outline
2-1
2-2
2-3
2-4
2
Organizing Data
Histograms, Frequency Polygons, and Ogives
Other Types of Graphs
Paired Data and Scatter Plots
CHAPTER
Frequency Distributions and Graphs
Objectives
1
2
3
4
5
2
Organize data using a frequency distribution.
Represent data in frequency distributions graphically
using histograms, frequency polygons, and ogives.
Represent data using bar graphs, Pareto charts, time
series graphs, and pie graphs.
Draw and interpret a stem and leaf plot.
Draw and interpret a scatter plot for a set of paired
data.
2-1 Organizing Data

Data collected in original form is called
raw data.

A frequency distribution is the
organization of raw data in table form,
using classes and frequencies.

Nominal- or ordinal-level data that can be
placed in categories is organized in
categorical frequency distributions.
Bluman, Chapter 2
4
Chapter 2
Frequency Distributions and
Graphs
Section 2-1
Example 2-1
Page #38
Bluman, Chapter 2
5
Categorical Frequency Distribution
Twenty-five army inductees were given a blood
test to determine their blood type.
Raw Data: A,B,B,AB,O
O,O,B,AB,B
B,B,O,A,O
A,O,O,O,AB
AB,A,O,B,A
Construct a frequency distribution for the data.
Bluman, Chapter 2
6
Categorical Frequency Distribution
Twenty-five army inductees were given a blood
test to determine their blood type.
Raw Data: A,B,B,AB,O
O,O,B,AB,B
B,B,O,A,O
A,O,O,O,AB
AB,A,O,B,A
Class Tally
A
B
O
AB
IIII
IIII II
IIII IIII
IIII
Frequency Percent
5
7
9
4
Bluman, Chapter 2
20
28
36
16
7
Grouped Frequency Distribution

Grouped frequency distributions are
used when the range of the data is large.

The smallest and largest possible data
values in a class are the lower and
upper class limits. Class boundaries
separate the classes.

To find a class boundary, average the
upper class limit of one class and the
lower class limit of the next class.
Bluman, Chapter 2
8
Grouped Frequency Distribution

The class width can be calculated by
subtracting
 successive
lower class limits (or boundaries)
 successive upper class limits (or boundaries)
 upper and lower class boundaries

The class midpoint Xm can be calculated
by averaging
 upper
and lower class limits (or boundaries)
Bluman, Chapter 2
9
Rules for Classes in Grouped
Frequency Distributions
1.
2.
3.
4.
5.
6.
There should be 5-20 classes.
The class width should be an odd
number.
The classes must be mutually exclusive.
The classes must be continuous.
The classes must be exhaustive.
The classes must be equal in width
(except in open-ended distributions).
Bluman, Chapter 2
10
Chapter 2
Frequency Distributions and
Graphs
Section 2-1
Example 2-2
Page #41
Bluman, Chapter 2
11
Constructing a Grouped Frequency
Distribution
The following data represent the record
high temperatures for each of the 50 states.
Construct a grouped frequency distribution
for the data using 7 classes.
112
110
107
116
120
100
118
112
108
113
127
117
114
110
120
120
116
115
121
117
134
118
118
113
105
118
122
117
120
110
Bluman, Chapter 2
105
114
118
119
118
110
114
122
111
112
109
105
106
104
114
112
109
110
111
114
12
Constructing a Grouped Frequency
Distribution
STEP 1 Determine the classes.
Find the class width by dividing the range by
the number of classes 7.
Range = High – Low
= 134 – 100 = 34
Width = Range/7 = 34/7 = 5
Rounding Rule: Always round up if a remainder.
Bluman, Chapter 2
13
Constructing a Grouped Frequency
Distribution
 For
convenience sake, we will choose the lowest
data value, 100, for the first lower class limit.
 The subsequent lower class limits are found by
adding the width to the previous lower class limits.
Class Limits
100 – 104
105 – 109
110 – 114
115 – 119
120 – 124
125 – 129
130 – 134
The
first upper class limit is one
less than the next lower class limit.
The
subsequent upper class limits
are found by adding the width to the
previous upper class limits.
Bluman, Chapter 2
14
Constructing a Grouped Frequency
Distribution
 The
class boundary is midway between an upper
class limit and a subsequent lower class limit.
104,104.5,105
Class
Limits
Class
Boundaries
100 – 104
105 – 109
110 – 114
115 – 119
120 – 124
125 – 129
130 – 134
99.5 – 104.5
104.5 – 109.5
109.5 – 114.5
114.5 – 119.5
119.5 – 124.5
124.5 – 129.5
129.5 – 134.5
Frequency
Bluman, Chapter 2
Cumulative
Frequency
15
Constructing a Grouped Frequency
Distribution
STEP 2 Tally the data.
STEP 3 Find the frequencies.
Class
Limits
Class
Boundaries
100 – 104
105 – 109
110 – 114
115 – 119
120 – 124
125 – 129
130 – 134
99.5 – 104.5
104.5 – 109.5
109.5 – 114.5
114.5 – 119.5
119.5 – 124.5
124.5 – 129.5
129.5 – 134.5
Cumulative
Frequency
Frequency
Bluman, Chapter 2
2
8
18
13
7
1
1
16
Constructing a Grouped Frequency
Distribution
STEP 4 Find the cumulative frequencies by
keeping a running total of the frequencies.
Class
Limits
Class
Boundaries
Frequency
Cumulative
Frequency
100 – 104
105 – 109
110 – 114
115 – 119
120 – 124
125 – 129
130 – 134
99.5 – 104.5
104.5 – 109.5
109.5 – 114.5
114.5 – 119.5
119.5 – 124.5
124.5 – 129.5
129.5 – 134.5
2
8
18
13
7
1
1
2
10
28
41
48
49
50
Bluman, Chapter 2
17
2-2 Histograms, Frequency
Polygons, and Ogives
3 Most Common Graphs in Research
1. Histogram
2. Frequency
Polygon
3. Cumulative
Frequency Polygon (Ogive)
Bluman, Chapter 2
18
2-2 Histograms, Frequency
Polygons, and Ogives
The histogram is a graph that
displays the data by using vertical
bars of various heights to represent
the frequencies of the classes.
The class boundaries are
represented on the horizontal axis.
Bluman, Chapter 2
19
Chapter 2
Frequency Distributions and
Graphs
Section 2-2
Example 2-4
Page #51
Bluman, Chapter 2
20
Histograms
Construct a histogram to represent the
data for the record high temperatures for
each of the 50 states (see Example 2–2 for
the data).
Bluman, Chapter 2
21
Histograms
Histograms use class boundaries and
frequencies of the classes.
Class
Limits
Class
Boundaries
Frequency
100 – 104
105 – 109
110 – 114
115 – 119
120 – 124
125 – 129
130 – 134
99.5 – 104.5
104.5 – 109.5
109.5 – 114.5
114.5 – 119.5
119.5 – 124.5
124.5 – 129.5
129.5 – 134.5
2
8
18
13
7
1
1
Bluman, Chapter 2
22
Histograms
Histograms use class boundaries and
frequencies of the classes.
Bluman, Chapter 2
23
2.2 Histograms, Frequency
Polygons, and Ogives
The frequency polygon is a graph that
displays the data by using lines that
connect points plotted for the
frequencies at the class midpoints. The
frequencies are represented by the
heights of the points.
 The class midpoints are represented on
the horizontal axis.

Bluman, Chapter 2
24
Chapter 2
Frequency Distributions and
Graphs
Section 2-2
Example 2-5
Page #53
Bluman, Chapter 2
25
Frequency Polygons
Construct a frequency polygon to
represent the data for the record high
temperatures for each of the 50 states
(see Example 2–2 for the data).
Bluman, Chapter 2
26
Frequency Polygons
Frequency polygons use class midpoints
and frequencies of the classes.
Class
Limits
Class
Midpoints
Frequency
100 – 104
105 – 109
110 – 114
115 – 119
120 – 124
125 – 129
130 – 134
102
107
112
117
122
127
132
2
8
18
13
7
1
1
Bluman, Chapter 2
27
Frequency Polygons
Frequency polygons use class midpoints
and frequencies of the classes.
A frequency polygon
is anchored on the
x-axis before the first
class and after the
last class.
Bluman, Chapter 2
28
2.2 Histograms, Frequency
Polygons, and Ogives

The ogive is a graph that represents
the cumulative frequencies for the
classes in a frequency distribution.

The upper class boundaries are
represented on the horizontal axis.
Bluman, Chapter 2
29
Chapter 2
Frequency Distributions and
Graphs
Section 2-2
Example 2-6
Page #54
Bluman, Chapter 2
30
Ogives
Construct an ogive to represent the data
for the record high temperatures for each
of the 50 states (see Example 2–2 for the
data).
Bluman, Chapter 2
31
Ogives
Ogives use upper class boundaries and
cumulative frequencies of the classes.
Class
Limits
Class
Boundaries
100 – 104
105 – 109
110 – 114
115 – 119
120 – 124
125 – 129
130 – 134
99.5 – 104.5
104.5 – 109.5
109.5 – 114.5
114.5 – 119.5
119.5 – 124.5
124.5 – 129.5
129.5 – 134.5
Cumulative
Frequency
Frequency
Bluman, Chapter 2
2
8
18
13
7
1
1
2
10
28
41
48
49
50
32
Ogives
Ogives use upper class boundaries and
cumulative frequencies of the classes.
Class Boundaries
Cumulative
Frequency
Less than 104.5
Less than 109.5
Less than 114.5
Less than 119.5
Less than 124.5
Less than 129.5
Less than 134.5
2
10
28
41
48
49
50
Bluman, Chapter 2
33
Ogives
Ogives use upper class boundaries and
cumulative frequencies of the classes.
Bluman, Chapter 2
34
Procedure Table
Constructing Statistical Graphs
Step 1
Draw and label the x and y axes.
Step 2
Choose a suitable scale for the frequencies or
cumulative frequencies, and label it on the y axis.
Step 3
Represent the class boundaries for the histogram or
ogive, or the midpoint for the frequency polygon,
on the x axis.
Step 4
Plot the points and then draw the bars or lines.
2.2 Histograms, Frequency
Polygons, and Ogives
If proportions are used instead of
frequencies, the graphs are called
relative frequency graphs.
Relative frequency graphs are used
when the proportion of data values that
fall into a given class is more important
than the actual number of data values
that fall into that class.
Bluman, Chapter 2
36
Chapter 2
Frequency Distributions and
Graphs
Section 2-2
Example 2-7
Page #57
Bluman, Chapter 2
37
Construct a histogram, frequency polygon,
and ogive using relative frequencies for the
distribution (shown here) of the miles that
20 randomly selected runners ran during a
given week.
Class
Frequency
Boundaries
5.5 – 10.5
10.5 – 15.5
15.5 – 20.5
20.5 – 25.5
25.5 – 30.5
30.5 – 35.5
35.5 – 40.5
Bluman, Chapter 2
1
2
3
5
4
3
2
38
Histograms
The following is a frequency distribution of
miles run per week by 20 selected runners.
Class
Frequency
Boundaries
5.5 – 10.5
1
10.5 – 15.5
2
15.5 – 20.5
3
20.5 – 25.5
5
25.5 – 30.5
4
30.5 – 35.5
3
35.5 – 40.5
2
f = 20
Relative
Frequency
1/20 = 0.05
2/20 = 0.10
3/20 = 0.15
5/20 = 0.25
4/20 = 0.20
3/20 = 0.15
2/20 = 0.10
rf = 1.00
Bluman, Chapter 2
Divide each
frequency
by the total
frequency to
get the
relative
frequency.
39
Histograms
Use the class boundaries and the
relative frequencies of the classes.
Bluman, Chapter 2
40
Frequency Polygons
The following is a frequency distribution of
miles run per week by 20 selected runners.
Class
Class
Relative
Boundaries Midpoints Frequency
5.5 – 10.5
8
0.05
10.5 – 15.5
13
0.10
15.5 – 20.5
18
0.15
20.5 – 25.5
23
0.25
25.5 – 30.5
28
0.20
30.5 – 35.5
33
0.15
35.5 – 40.5
38
0.10
Bluman, Chapter 2
41
Frequency Polygons
Use the class midpoints and the
relative frequencies of the classes.
Bluman, Chapter 2
42
Ogives
The following is a frequency distribution of
miles run per week by 20 selected runners.
Class
Frequency
Boundaries
5.5 – 10.5
1
10.5 – 15.5
2
15.5 – 20.5
3
20.5 – 25.5
5
25.5 – 30.5
4
30.5 – 35.5
3
35.5 – 40.5
2
f = 20
Cumulative
Frequency
1
3
6
11
15
18
20
Bluman, Chapter 2
Cum. Rel.
Frequency
1/20 =
3/20 =
6/20 =
11/20 =
15/20 =
18/20 =
20/20 =
0.05
0.15
0.30
0.55
0.75
0.90
1.00
43
Ogives
Ogives use upper class boundaries and
cumulative frequencies of the classes.
Class Boundaries
Cum. Rel.
Frequency
Less than 10.5
Less than 15.5
Less than 20.5
Less than 25.5
Less than 30.5
Less than 35.5
Less than 40.5
0.05
0.15
0.30
0.55
0.75
0.90
1.00
Bluman, Chapter 2
44
Ogives
Use the upper class boundaries and the
cumulative relative frequencies.
Bluman, Chapter 2
45
Shapes of Distributions
Bluman, Chapter 2
46
Shapes of Distributions
Bluman, Chapter 2
47
2.3 Other Types of Graphs
Bar Graphs
Bluman, Chapter 2
48
2.3 Other Types of Graphs
Pareto Charts
Bluman, Chapter 2
49
2.3 Other Types of Graphs
Time Series Graphs
Bluman, Chapter 2
50
2.3 Other Types of Graphs
Pie Graphs
Bluman, Chapter 2
51
2.3 Other Types of Graphs
Stem and Leaf Plots
A stem and leaf plot is a data plot that
uses part of a data value as the stem
and part of the data value as the leaf to
form groups or classes.
It has the advantage over grouped
frequency distribution of retaining the
actual data while showing them in
graphic form.
Bluman, Chapter 2
52
Chapter 2
Frequency Distributions and
Graphs
Section 2-3
Example 2-13
Page #80
Bluman, Chapter 2
53
At an outpatient testing center, the
number of cardiograms performed each
day for 20 days is shown. Construct a
stem and leaf plot for the data.
25
14
36
32
31
43
32
52
20
2
33
44
32
57
32
51
Bluman, Chapter 2
13
23
44
45
54
25
14
36
32
31
43
32
52
Unordered Stem Plot
20
2
33
44
32
57
32
51
13
23
44
45
Ordered Stem Plot
0 2
0 2
1 3 4
1
2
3
4
2
3
4
5
5
1
3
7
0
2
4
2
3
6 2 3 2 2
4 5
1
3
0
1
3
4
3 5
2 2 2 2 3 6
4 4 5
5 1 2 7
Bluman, Chapter 2
55
2.4 Paired Data and Scatter
Plots
A scatter plot is a graph of order pairs
of data values that is used to determine
if a relationship exists between the two
variables.
Bluman, Chapter 2
56
Chapter 2
Frequency Distributions and
Graphs
Section 2-4
Example 2-16
Page #95
Bluman, Chapter 2
57
A researcher is interested in determining if
there is a relationship between the number of
wet bike accidents and the number of wet
bike fatalities. The data are for a 10-year
period. Draw a scatter plot for the data.
Bluman, Chapter 2
58
Step 1 Draw and label the x and y axes.
Step 2 Plot the points for pairs of data.
Bluman, Chapter 2
59
2.4 Paired Data and Scatter
Plots
Analyzing the Scatter Plot
1. A positive linear relationship exists when the points fall
approximately in an ascending straight line and both the x and
y values increase at the same time.
Bluman, Chapter 2
60
2.4 Paired Data and Scatter
Plots
Analyzing the Scatter Plot
2. A negative linear relationship exists when the points fall
approximately in a descending straight line from left to right.
Bluman, Chapter 2
61
2.4 Paired Data and Scatter
Plots
Analyzing the Scatter Plot
3. A nonlinear relationship exists when the points fall in a
curved line.
Bluman, Chapter 2
62
2.4 Paired Data and Scatter
Plots
Analyzing the Scatter Plot
4. No relationship exists when there is no discernible pattern of
the points.
Bluman, Chapter 2
63
Week 1 Internet Resources
Resources from the Internet can be valuable supplementary resources for
self-study. One of the most widely acclaimed resources is the “ Kahn
Academy” which has a large library of short videos on math and other
topics. The following is a list of Kahn Academy videos about topics
covered in this week’s lessons. You may wish to explore this resource on
your own, if you see fit.
1
Click here to view the video titled Graphing a Line in Slope-intercept
Form.
2
Click here to view the video titled Linear Equation from Slope and a
Point.
3
4
5
Week 1 e-Activity
Statistician Nate Silver became famous in 2008 when he correctly
predicted the Presidential Election in 49 of the 50 states. Mr. Silver has
done more than just predicting elections. Visit Nate Silver’s blog,
located at http://fivethirtyeight.blogs.nytimes.com/, and read one blog
entry that is related to one of this week’s topics. Be prepared to
discuss.
6
Articles and Websites to Review for Week 1
on Week 1.
7
The Importance of Statistics in Management
Decision Making – John T. Williams
8
Innovators, How Do You Use Data? – Scott
Anthony
9
Big data: The next frontier for innovation,
competition, and productivity – McKinsey and
Company
10
WHAT IS STATISTICS?
Watch Video
11

12

13
Summation of Indexed Data
Watch Video
14

15

16
Writing the equation of a line given y-
intercept and another point
Watch Video
17

18

19
Graphing a line given its equation in slope-
intercept form
Watch Video

20

21

22
Graphing a line through a given point with
a given slope

Watch Video

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