Introduction
I
Latin word “status” meaning “state”
Introduction
I
Latin word “status” meaning “state”
I
The discipline of statistics probides methods for organizing
and summarizing data and for drawing conclusions based on
information contained in the data.
Introduction
I
Latin word “status” meaning “state”
I
The discipline of statistics probides methods for organizing
and summarizing data and for drawing conclusions based on
information contained in the data.
I
Our Focus: Drawing Conclusions or Making Statistical
Inferences
Basic Concepts
Basic Concepts
I
Population: total collection of objects we are interested in
Basic Concepts
I
Population: total collection of objects we are interested in
I
Sample: a subset of the population
Basic Concepts
I
Population: total collection of objects we are interested in
I
Sample: a subset of the population
I
Census: information for all objects in the population
Basic Concepts
I
Population: total collection of objects we are interested in
I
Sample: a subset of the population
I
Census: information for all objects in the population
I
Examples:
Basic Concepts
I
Population: total collection of objects we are interested in
I
Sample: a subset of the population
I
Census: information for all objects in the population
I
Examples:
Number of students in this classroom who drove here today
Basic Concepts
I
Population: total collection of objects we are interested in
I
Sample: a subset of the population
I
Census: information for all objects in the population
I
Examples:
Number of students in this classroom who drove here today
Population: all the students in the class room;
Sample: All the boy; Census: possible
Basic Concepts
I
Population: total collection of objects we are interested in
I
Sample: a subset of the population
I
Census: information for all objects in the population
I
Examples:
Number of students in this classroom who drove here today
Population: all the students in the class room;
Sample: All the boy; Census: possible
GE manufactured 100,000,000 lamps. What’s life range?
Basic Concepts
I
Population: total collection of objects we are interested in
I
Sample: a subset of the population
I
Census: information for all objects in the population
I
Examples:
Number of students in this classroom who drove here today
Population: all the students in the class room;
Sample: All the boy; Census: possible
GE manufactured 100,000,000 lamps. What’s life range?
Population: 100,000,000 lamps; Sample: randomly
selected 1,000 lamps; Census: impossible
Basic Concepts
Basic Concepts
I
Variable: a characteristic of the population that may differ
from individual to individual
Basic Concepts
I
Variable: a characteristic of the population that may differ
from individual to individual
usually use lowercase letters to denote variables
Basic Concepts
I
Variable: a characteristic of the population that may differ
from individual to individual
usually use lowercase letters to denote variables
Examples: x = yes or no a student drove to school today
y = maximum hours a lamp can last
Basic Concepts
I
I
Variable: a characteristic of the population that may differ
from individual to individual
usually use lowercase letters to denote variables
Examples: x = yes or no a student drove to school today
y = maximum hours a lamp can last
Univariate Data: observation on a single variable
Basic Concepts
I
Variable: a characteristic of the population that may differ
from individual to individual
usually use lowercase letters to denote variables
Examples: x = yes or no a student drove to school today
y = maximum hours a lamp can last
Univariate Data: observation on a single variable
I
Bivariate Data: observation on each of two variables
I
Basic Concepts
I
Variable: a characteristic of the population that may differ
from individual to individual
usually use lowercase letters to denote variables
Examples: x = yes or no a student drove to school today
y = maximum hours a lamp can last
Univariate Data: observation on a single variable
I
Bivariate Data: observation on each of two variables
I
Multivariate Data: observations made on more than one
variable
I
Basic Concepts
I
Variable: a characteristic of the population that may differ
from individual to individual
usually use lowercase letters to denote variables
Examples: x = yes or no a student drove to school today
y = maximum hours a lamp can last
Univariate Data: observation on a single variable
I
Bivariate Data: observation on each of two variables
I
Multivariate Data: observations made on more than one
variable
I
Examples:
The collection of data about whether students drove to school
today and the gender of students
I
Basic Concepts
I
Variable: a characteristic of the population that may differ
from individual to individual
usually use lowercase letters to denote variables
Examples: x = yes or no a student drove to school today
y = maximum hours a lamp can last
Univariate Data: observation on a single variable
I
Bivariate Data: observation on each of two variables
I
Multivariate Data: observations made on more than one
variable
I
Examples:
The collection of data about whether students drove to school
today and the gender of students
The collection of data about whether students drove to school
today, the gender of students and the distance from their
home to campus
I
Basic Concepts
Basic Concepts
I
Conceptual/Hypothetical Population: population which
does not physically exist
Basic Concepts
I
Conceptual/Hypothetical Population: population which
does not physically exist
Examples: all possible values of tomorrow’s highest
temperature; all possible pH values of some unknown liquid;
etc.
Basic Concepts
I
Conceptual/Hypothetical Population: population which
does not physically exist
Examples: all possible values of tomorrow’s highest
temperature; all possible pH values of some unknown liquid;
etc.
I
Enumerative v.s. Analytic Studies
Basic Concepts
I
Conceptual/Hypothetical Population: population which
does not physically exist
Examples: all possible values of tomorrow’s highest
temperature; all possible pH values of some unknown liquid;
etc.
I
Enumerative v.s. Analytic Studies
Enumerative Studies: the sample is available to an
investigator or else can be constructed
Basic Concepts
I
Conceptual/Hypothetical Population: population which
does not physically exist
Examples: all possible values of tomorrow’s highest
temperature; all possible pH values of some unknown liquid;
etc.
I
Enumerative v.s. Analytic Studies
Enumerative Studies: the sample is available to an
investigator or else can be constructed
Examples: life of the GE lamps; the gender of students in this
classroom
Basic Concepts
I
Conceptual/Hypothetical Population: population which
does not physically exist
Examples: all possible values of tomorrow’s highest
temperature; all possible pH values of some unknown liquid;
etc.
I
Enumerative v.s. Analytic Studies
Enumerative Studies: the sample is available to an
investigator or else can be constructed
Examples: life of the GE lamps; the gender of students in this
classroom
Analytic Studies: the sample is NOT available
Basic Concepts
I
Conceptual/Hypothetical Population: population which
does not physically exist
Examples: all possible values of tomorrow’s highest
temperature; all possible pH values of some unknown liquid;
etc.
I
Enumerative v.s. Analytic Studies
Enumerative Studies: the sample is available to an
investigator or else can be constructed
Examples: life of the GE lamps; the gender of students in this
classroom
Analytic Studies: the sample is NOT available
Examples: tomorrow’s highest temperature; Champion of the
2009 NBA
Basic Concepts
Basic Concepts
I
Descriptive Statistics & Inferential Statistics
Basic Concepts
I
Descriptive Statistics & Inferential Statistics
Recall: The discipline of statistics probides methods for organizing
and summarizing data and for drawing conclusions based on
information contained in the data.
Basic Concepts
I
Descriptive Statistics & Inferential Statistics
Recall: The discipline of statistics probides methods for organizing
and summarizing data and for drawing conclusions based on
information contained in the data.
I
Descriptive Statistics: discipline of organizing and
summarizing data
Basic Concepts
I
Descriptive Statistics & Inferential Statistics
Recall: The discipline of statistics probides methods for organizing
and summarizing data and for drawing conclusions based on
information contained in the data.
I
Descriptive Statistics: discipline of organizing and
summarizing data
I
Inferential Statistics: discipline of drawing conclusions from
a sample to a population
Basic Concepts
I Example(Example 1.2 p5): The article ‘‘Effects of Aggregates and
Microfillers on the Flexural Properties of Concrete’’ reported on a
study of strength properties of high performance concrete obtained by using
superplasticizers and certain binders. The accompanying data on flexural
strength (in MPa) appeared in the article cited:
5.9
7.2
7.3
6.3
8.1
6.8
7.0
7.6
6.8
6.5
7.0
6.3
7.9
9.0
8.2
8.7
7.8
9.7
7.4
7.7
9.7
7.8
7.7
11.6
11.3
11.8
10.7
We are interested in the average value of flexural strength for all beams that
could be made in this way.
Basic Concepts
I Example(Example 1.2 p5): The article ‘‘Effects of Aggregates and
Microfillers on the Flexural Properties of Concrete’’ reported on a
study of strength properties of high performance concrete obtained by using
superplasticizers and certain binders. The accompanying data on flexural
strength (in MPa) appeared in the article cited:
5.9
7.2
7.3
6.3
8.1
6.8
7.0
7.6
6.8
6.5
7.0
6.3
7.9
9.0
8.2
8.7
7.8
9.7
7.4
7.7
9.7
7.8
7.7
11.6
11.3
11.8
10.7
We are interested in the average value of flexural strength for all beams that
could be made in this way.
The stem-and-leaf plot:
Basic Concepts
I Example(Example 1.2 p5): The article ‘‘Effects of Aggregates and
Microfillers on the Flexural Properties of Concrete’’ reported on a
study of strength properties of high performance concrete obtained by using
superplasticizers and certain binders. The accompanying data on flexural
strength (in MPa) appeared in the article cited:
5.9
7.2
7.3
6.3
8.1
6.8
7.0
7.6
6.8
6.5
7.0
6.3
7.9
9.0
8.2
8.7
7.8
9.7
7.4
7.7
9.7
7.8
7.7
11.6
11.3
11.8
10.7
We are interested in the average value of flexural strength for all beams that
could be made in this way.
The stem-and-leaf plot:
5 |
9
6 |
33588
7 |
00234677889
8 |
127
9 |
077
10 |
7
11 |
368
Basic Concepts
I Example(Example 1.2 p5): The article ‘‘Effects of Aggregates and
Microfillers on the Flexural Properties of Concrete’’ reported on a
study of strength properties of high performance concrete obtained by using
superplasticizers and certain binders. The accompanying data on flexural
strength (in MPa) appeared in the article cited:
5.9
7.2
7.3
6.3
8.1
6.8
7.0
7.6
6.8
6.5
7.0
6.3
7.9
9.0
8.2
8.7
7.8
9.7
7.4
7.7
9.7
7.8
7.7
11.6
11.3
11.8
10.7
We are interested in the average value of flexural strength for all beams that
could be made in this way.
The stem-and-leaf plot:
The histogram graph:
5 |
9
6 |
33588
7 |
00234677889
8 |
127
9 |
077
10 |
7
11 |
368
Basic Concepts
I Example(Example 1.2 p5): The article ‘‘Effects of Aggregates and
Microfillers on the Flexural Properties of Concrete’’ reported on a
study of strength properties of high performance concrete obtained by using
superplasticizers and certain binders. The accompanying data on flexural
strength (in MPa) appeared in the article cited:
5.9
7.2
7.3
6.3
8.1
6.8
7.0
7.6
6.8
6.5
7.0
6.3
7.9
9.0
8.2
8.7
7.8
9.7
7.4
7.7
9.7
7.8
7.7
11.6
11.3
11.8
10.7
We are interested in the average value of flexural strength for all beams that
could be made in this way.
The stem-and-leaf plot:
The histogram graph:
5 |
9
6 |
33588
7 |
00234677889
8 |
127
9 |
077
10 |
7
11 |
368
Basic Concepts
I Example(Example 1.2 p5): The article ‘‘Effects of Aggregates and
Microfillers on the Flexural Properties of Concrete’’ reported
on a study of strength properties of high performance concrete obtained
by using superplasticizers and certain binders. The accompanying data on
flexural strength (in MPa) appeared in the article cited:
5.9 7.2 7.3 6.3 8.1
6.8
7.0
7.6
6.8
6.5 7.0 6.3 7.9 9.0
8.2
8.7
7.8
9.7
7.4 7.7 9.7 7.8 7.7 11.6 11.3 11.8 10.7
We are interested in the average value of flexural strength for all beams
that could be made in this way.
Basic Concepts
I Example(Example 1.2 p5): The article ‘‘Effects of Aggregates and
Microfillers on the Flexural Properties of Concrete’’ reported
on a study of strength properties of high performance concrete obtained
by using superplasticizers and certain binders. The accompanying data on
flexural strength (in MPa) appeared in the article cited:
5.9 7.2 7.3 6.3 8.1
6.8
7.0
7.6
6.8
6.5 7.0 6.3 7.9 9.0
8.2
8.7
7.8
9.7
7.4 7.7 9.7 7.8 7.7 11.6 11.3 11.8 10.7
We are interested in the average value of flexural strength for all beams
that could be made in this way.
Moreover, we can make statistical inferences from this data set.
Basic Concepts
I Example(Example 1.2 p5): The article ‘‘Effects of Aggregates and
Microfillers on the Flexural Properties of Concrete’’ reported
on a study of strength properties of high performance concrete obtained
by using superplasticizers and certain binders. The accompanying data on
flexural strength (in MPa) appeared in the article cited:
5.9 7.2 7.3 6.3 8.1
6.8
7.0
7.6
6.8
6.5 7.0 6.3 7.9 9.0
8.2
8.7
7.8
9.7
7.4 7.7 9.7 7.8 7.7 11.6 11.3 11.8 10.7
We are interested in the average value of flexural strength for all beams
that could be made in this way.
Moreover, we can make statistical inferences from this data set.
It can be shown that, with a high degree of confidence, the population
mean strength is between 7.48 MPa and 8.80 Mpa; this is called a
confidence interval or interval.
Basic Concepts
I Example(Example 1.2 p5): The article ‘‘Effects of Aggregates and
Microfillers on the Flexural Properties of Concrete’’ reported
on a study of strength properties of high performance concrete obtained
by using superplasticizers and certain binders. The accompanying data on
flexural strength (in MPa) appeared in the article cited:
5.9 7.2 7.3 6.3 8.1
6.8
7.0
7.6
6.8
6.5 7.0 6.3 7.9 9.0
8.2
8.7
7.8
9.7
7.4 7.7 9.7 7.8 7.7 11.6 11.3 11.8 10.7
We are interested in the average value of flexural strength for all beams
that could be made in this way.
Moreover, we can make statistical inferences from this data set.
It can be shown that, with a high degree of confidence, the population
mean strength is between 7.48 MPa and 8.80 Mpa; this is called a
confidence interval or interval.
Furthermore, with a high degree of confidence, the strength of a single
such beam will exceed 7.35 MPa; this number 7.35 is called a lower
prediction bound.
Probability & Statistics
Probability & Statistics
Probability & Statistics
I
Probability: know the information of population and ask
question about sample
Probability & Statistics
I
Probability: know the information of population and ask
question about sample
A probability question: We have a fair coin and toss it many
times. What’s the chance to get three consecutive heads?
Probability & Statistics
I
Probability: know the information of population and ask
question about sample
A probability question: We have a fair coin and toss it many
times. What’s the chance to get three consecutive heads?
I
Statistics: know the information of sample and ask question
about population
Probability & Statistics
I
Probability: know the information of population and ask
question about sample
A probability question: We have a fair coin and toss it many
times. What’s the chance to get three consecutive heads?
I
Statistics: know the information of sample and ask question
about population
A statistic question: We have a coin and toss it 6 times. The
results are THT,THH, HTT, HTH, TTH and HTT. Is this
coin a fair coin?
Pictorial and Tabular Methods
I
Example(Example 1.2 p5): The article ‘‘Effects of
Aggregates and Microfillers on the Flexural
Properties of Concrete’’ reported on a study of strength
properties of high performance concrete obtained by using
superplasticizers and certain binders. The accompanying data
on flexural strength (in MPa) appeared in the article cited:
5.9 7.2 7.3 6.3 8.1
6.8
7.0
7.6
6.8
6.5 7.0 6.3 7.9 9.0
8.2
8.7
7.8
9.7
7.4 7.7 9.7 7.8 7.7 11.6 11.3 11.8 10.7
We are interested in the average value of flexural strength for
all beams that could be made in this way.
Pictorial and Tabular Methods
5.9
6.5
7.4
7.2
7.0
7.7
7.3
6.3
9.7
6.3
7.9
7.8
8.1
9.0
7.7
6.8
8.2
11.6
7.0
8.7
11.3
7.6
7.8
11.8
6.8
9.7
10.7
Pictorial and Tabular Methods
5.9
6.5
7.4
7.2
7.0
7.7
7.3
6.3
9.7
6.3
7.9
7.8
8.1
9.0
7.7
6.8
8.2
11.6
The decimal point is at the |
7.0
8.7
11.3
7.6
7.8
11.8
6.8
9.7
10.7
Pictorial and Tabular Methods
5.9
6.5
7.4
7.2
7.0
7.7
7.3
6.3
9.7
6.3
7.9
7.8
8.1
9.0
7.7
6.8
8.2
11.6
The decimal point is at the |
5
|
9
7.0
8.7
11.3
7.6
7.8
11.8
6.8
9.7
10.7
Pictorial and Tabular Methods
5.9
6.5
7.4
7.2
7.0
7.7
7.3
6.3
9.7
6.3
7.9
7.8
8.1
9.0
7.7
6.8
8.2
11.6
The decimal point is at the |
5
6
|
|
9
33588
7.0
8.7
11.3
7.6
7.8
11.8
6.8
9.7
10.7
Pictorial and Tabular Methods
5.9
6.5
7.4
7.2
7.0
7.7
7.3
6.3
9.7
6.3
7.9
7.8
8.1
9.0
7.7
6.8
8.2
11.6
The decimal point is at the |
5
6
7
|
|
|
9
33588
00234677889
7.0
8.7
11.3
7.6
7.8
11.8
6.8
9.7
10.7
Pictorial and Tabular Methods
5.9
6.5
7.4
7.2
7.0
7.7
7.3
6.3
9.7
6.3
7.9
7.8
8.1
9.0
7.7
6.8
8.2
11.6
The decimal point is at the |
5
6
7
8
|
|
|
|
9
33588
00234677889
127
7.0
8.7
11.3
7.6
7.8
11.8
6.8
9.7
10.7
Pictorial and Tabular Methods
5.9
6.5
7.4
7.2
7.0
7.7
7.3
6.3
9.7
6.3
7.9
7.8
8.1
9.0
7.7
6.8
8.2
11.6
The decimal point is at the |
5
6
7
8
9
|
|
|
|
|
9
33588
00234677889
127
077
7.0
8.7
11.3
7.6
7.8
11.8
6.8
9.7
10.7
Pictorial and Tabular Methods
5.9
6.5
7.4
7.2
7.0
7.7
7.3
6.3
9.7
6.3
7.9
7.8
8.1
9.0
7.7
6.8
8.2
11.6
The decimal point is at the |
5
6
7
8
9
10
|
|
|
|
|
|
9
33588
00234677889
127
077
7
7.0
8.7
11.3
7.6
7.8
11.8
6.8
9.7
10.7
Pictorial and Tabular Methods
5.9
6.5
7.4
7.2
7.0
7.7
7.3
6.3
9.7
6.3
7.9
7.8
8.1
9.0
7.7
6.8
8.2
11.6
The decimal point is at the |
5
6
7
8
9
10
11
|
|
|
|
|
|
|
9
33588
00234677889
127
077
7
368
7.0
8.7
11.3
7.6
7.8
11.8
6.8
9.7
10.7
Pictorial and Tabular Methods
5.9
6.5
7.4
7.2
7.0
7.7
7.3
6.3
9.7
6.3
7.9
7.8
8.1
9.0
7.7
6.8
8.2
11.6
7.0
8.7
11.3
7.6
7.8
11.8
6.8
9.7
10.7
The decimal point is at the |
5
6
7
8
9
10
11
|
|
|
|
|
|
|
9
33588
00234677889
127
077
7
368
• identification of a typical
value
Pictorial and Tabular Methods
5.9
6.5
7.4
7.2
7.0
7.7
7.3
6.3
9.7
6.3
7.9
7.8
8.1
9.0
7.7
6.8
8.2
11.6
7.0
8.7
11.3
7.6
7.8
11.8
6.8
9.7
10.7
The decimal point is at the |
5
6
7
8
9
10
11
|
|
|
|
|
|
|
9
33588
00234677889
127
077
7
368
• identification of a typical
value
• presence of any gaps in the
data
Pictorial and Tabular Methods
5.9
6.5
7.4
7.2
7.0
7.7
7.3
6.3
9.7
6.3
7.9
7.8
8.1
9.0
7.7
6.8
8.2
11.6
7.0
8.7
11.3
7.6
7.8
11.8
6.8
9.7
10.7
The decimal point is at the |
5
6
7
8
9
10
11
|
|
|
|
|
|
|
9
33588
00234677889
127
077
7
368
• identification of a typical
value
• presence of any gaps in the
data
• extent of symmetry in the
distribution of values
Pictorial and Tabular Methods
5.9
6.5
7.4
7.2
7.0
7.7
7.3
6.3
9.7
6.3
7.9
7.8
8.1
9.0
7.7
6.8
8.2
11.6
7.0
8.7
11.3
7.6
7.8
11.8
6.8
9.7
10.7
The decimal point is at the |
5
6
7
8
9
10
11
|
|
|
|
|
|
|
9
33588
00234677889
127
077
7
368
• identification of a typical
value
• presence of any gaps in the
data
• extent of symmetry in the
distribution of values
• number and location of
peaks
Pictorial and Tabular Methods
5.9
6.5
7.4
7.2
7.0
7.7
7.3
6.3
9.7
6.3
7.9
7.8
8.1
9.0
7.7
6.8
8.2
11.6
7.0
8.7
11.3
7.6
7.8
11.8
6.8
9.7
10.7
The decimal point is at the |
5
6
7
8
9
10
11
|
|
|
|
|
|
|
9
33588
00234677889
127
077
7
368
• identification of a typical
value
• presence of any gaps in the
data
• extent of symmetry in the
distribution of values
• number and location of
peaks
• presence of any outlying
values
Pictorial and Tabular Methods
Pictorial and Tabular Methods
I
Stem-and-Leaf Displays
Pictorial and Tabular Methods
I
Stem-and-Leaf Displays
I
1. Select one or more leading digits for the stem values. The
trailing digits become the leaves.
Pictorial and Tabular Methods
I
Stem-and-Leaf Displays
I
1. Select one or more leading digits for the stem values. The
trailing digits become the leaves.
I
2. List possible stem values in a vertical column.
Pictorial and Tabular Methods
I
Stem-and-Leaf Displays
I
1. Select one or more leading digits for the stem values. The
trailing digits become the leaves.
I
2. List possible stem values in a vertical column.
I
3. Record the leaf for every observation beside the
corresponding stem value.
Pictorial and Tabular Methods
I
Stem-and-Leaf Displays
I
1. Select one or more leading digits for the stem values. The
trailing digits become the leaves.
I
2. List possible stem values in a vertical column.
I
3. Record the leaf for every observation beside the
corresponding stem value.
I
4. Indicate the units for stems and leaves someplace in the
display.
Pictorial and Tabular Methods
I
Remark:
Pictorial and Tabular Methods
I
Remark:
1. Each data in the population must consist of at least two
digits.
Pictorial and Tabular Methods
I
Remark:
1. Each data in the population must consist of at least two
digits.
e.g. the stem-and-leaf display is not suitable for the data set
1,2,1,4,1,5,2,6,1,3,2,3
Pictorial and Tabular Methods
I
Remark:
1. Each data in the population must consist of at least two
digits.
e.g. the stem-and-leaf display is not suitable for the data set
1,2,1,4,1,5,2,6,1,3,2,3
2. Ordering the leaves from smallest to largest is not necessary
Pictorial and Tabular Methods
The decimal point is at the |
5
6
7
8
9
10
11
|
|
|
|
|
|
|
9
38853
23060984787
127
077
7
638
The decimal point is at the |
5
6
7
8
9
10
11
|
|
|
|
|
|
|
9
33588
00234677889
127
077
7
368