“Statistics are Everywhere” (Note: Please respond to one [1] of the following two [2] 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

Letter Grade

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

Misleading Graphs

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

Click here to view the video titled Two-step Equations.

4

5

Click here to view the video titled Rounding Decimals.

Click here to view the video titled Order of Operations.

Click here to view the video titled Discrete versus Continuous Variables.

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

Click on the links below for additional information

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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