Chapter One
What is Statistics?
Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc.
1.1
FYI – Past Grades in This Statistics Course
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88
Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc.
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31
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33
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33
58
36
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36
50
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100
59
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32
33
40
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66
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45
43
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84
28
59
64
52
64
38
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34
62
26
28
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88
91
47
84
41
53
36
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43
72
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81
41
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36
24
37
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41
91
84
91
61
41
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43
42
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42
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77
58
66
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80
47
75
53
83
22
29
46
28
32
74
89
47
45
48
32
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67
23
83
60
25
34
98
22
64
75
81
88
87
83
37
86
73
20
23
78
47
86
42
86
37
43
79
81
56
62
66
64
92
70
57
54
77
39
58
36
55
81
62
40
87
33
61
33
43
52
99
99
85
60
65
28
81
41
86
78
26
84
81
88
74
94
66
94
57
54
24
57
20
23
44
36
82
34
70
47
94
65
84
79
68
98
53
39
53
27
54
25
23
59
85
48
89
81
45
91
92
80
48
88
74
92
24
81
49
82
47
1.2
FYI – Past Grades in This Statistics Course
Grades
0-10
10-20
20-30
30-40
40-50
50-60
60-70
70-80
80-90
90-100
Total =
Frequency Relative Freq
0
0.000
0
0.000
323
0.129
286
0.114
316
0.126
297
0.119
304
0.122
324
0.130
319
0.128
331
0.132
2500
Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc.
Percent
0.0%
0.0%
12.9%
11.4%
12.6%
11.9%
12.2%
13.0%
12.8%
13.2%
Cum Percent
0.0%
0.0%
12.9%
24.4%
37.0%
48.9%
61.0%
74.0%
86.8%
100.0%
1.3
FYI – Past Grades in This Statistics Course
400
200
0
010
10
-2
0
20
-3
0
30
-4
0
40
-5
0
50
-6
0
60
-7
0
70
-8
0
80
-9
90 0
-1
00
Frequency
Histogram
Final Grade
Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc.
1.4
In today’s world…
…we are constantly being bombarded with statistics and
statistical information. For example:
Customer Surveys Medical News
Political Polls Economic Predictions
Marketing Information Scanner Data
How can we make sense out of all this data?
How do we differentiate valid from flawed claims?
Three types of liars!
Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc.
1.5
What is Statistics? Where does this Data come from?
“Statistics is a way to get information from data”
Statistics
Data
Data: Facts, especially
numerical facts, collected
together for reference or
information.
Information
Information: Knowledge
communicated concerning
some particular fact.
Statistics is a tool for creating new understanding from a set of numbers.
Definitions: Oxford English Dictionary
Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc.
1.6
Key Statistical Concepts…
Population
— a population is the group of all items of interest to
a statistics practitioner.
— frequently very large; sometimes infinite.
E.g. All 5 million Florida voters who voted in today’s election.
Sample
— A sample is a set of data drawn from the
population. [Part of a population]
— Potentially very large, but less than the population.
E.g. a sample of 1000 voters exit polled on election day.
Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc.
1.7
Key Statistical Concepts…
Parameter
— A descriptive measure of a population.
- the true percent of Florida Voters who will vote for
Mary Poppins
Statistic
— A descriptive measure of a sample.
- Of the 1000 exit voters polled, 550 indicated that
they voted for Mary Poppins or 550/1000 = 0.55 or
55%
Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc.
1.8
Key Statistical Concepts…
Population
Sample
Subset
Parameter
Statistic
Populations have Parameters,
Samples have Statistics.
Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc.
1.9
Descriptive Statistics…
…are methods of organizing, summarizing, and presenting data in a
convenient and informative way. These methods include:
Graphical Techniques (Chapter 2), and
Numerical Techniques (Chapter 4).
The actual method used depends on what information we would like
to extract. Are we interested in…
• Your weight each Monday when you are on a 6 month diet.
• The amount of medication in blood pressure pills.
•The starting salaries for business students from TCU, SMU,
and UTA.
•Others…
Descriptive Statistics helps to answer these questions…
Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc.
1.10
Inferential Statistics…
Descriptive Statistics describe the data set that’s being
analyzed, but doesn’t allow us to draw any conclusions or
make any interferences about the data, other than visual “It
looks like …..” type statements. Hence we need another
branch of statistics: inferential statistics.
Inferential statistics is also a set of methods, but it is used to
draw conclusions or inferences about characteristics of
populations based on data from a sample.
Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc.
1.11
Statistical Inference…
Statistical inference is the process of making an estimate,
prediction, or decision about a population based on a sample.
Population
Sample
Inference
Statistic
Parameter
What can we infer about a Population’s Parameters
based on a Sample’s Statistics?
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1.12
Statistical Inference…
Rationale:
• Large populations make investigating each member impractical
and expensive + it’s been shown that observing 100% of a
population is not perfect.
• Easier and cheaper to take a sample and make inferences about
the population from the sample.
However:
Such conclusions and estimates are not always going to be correct.
For this reason, we build into the statistical inference “measures of
reliability”, namely confidence level and significance level.
Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc.
1.13
Confidence & Significance Levels…
The confidence level is the proportion of times that an interval estimate
for a population parameter will be correct.
E.g. a confidence level of 95% means that, interval estimates based on this form
of statistical inference will be correct 95% of the time.
I am 95% confident that the “TRUE” mean IQ of female business students at
UTA is between 120 and 122.
When the purpose of the statistical inference is to test a claim about a
population parameter, the significance level measures how frequently a
“true claim” is accidently rejected.
E.g. a 5% significance level means that, in the long run, a true claim will be
rejected 5% of the time.
Coin flips should result in 50% heads, on average. A 5% significance level
implies that we run a 5% risk of concluding that heads do not occur 50% of the
time, on average [even though everyone in this room most likely believes that
heads do occur 50% of the time].
Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc.
1.14
Confidence & Significance Levels…
We use  (Greek letter “alpha”) to represent the significance
level when testing a claim about a population parameter ,
and
1– to represent the confidence level when we wish to
estimate a population parameter.
Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc.
1.15
Statistical Applications in Business…
Statistical analysis plays an important role in virtually all
aspects of business and economics.
Throughout this course, we will see applications of statistics
in accounting, economics, finance, human resources
management, marketing, operations management, and my
favorite, “Quality Issues”,associated with manufacturing and
service processes.
Copyright © 2005 Brooks/Cole, a division of Thomson Learning, Inc.
1.16