Introduction
What is statistics?
“Utah Democrats are more sure. Thirty-six percent said Obama will take
the oath of office, 24 percent didn’t know, and 22 percent said it will be
Clinton.”
from Desert News:
It’s Utah’s turn:
Local voters favor Mitt and Obama, poll shows
R
“GE Spiral lamps:
long life – from 8,000 to 12,000 hours”
from http://www.geconsumerproducts.com/
“Dow Jones Industrial Average on Jun.5th”
from http://www.finance.yahoo.com/
Liang Zhang (UofU)
Applied Statistics I
June 9, 2008
1 / 10
Introduction
Latin word “status” meaning “state”
The discipline of statistics probides methods for organizing and
summarizing data and for drawing conclusions based on information
contained in the data.
Our Focus: Drawing Conclusions or Making Statistical Inferences
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Applied Statistics I
June 9, 2008
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Basic Concepts
Population: total collection of objects we are interested in
Sample: a subset of the population
Census: information for all objects in the population
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
Liang Zhang (UofU)
Applied Statistics I
June 9, 2008
3 / 10
Basic Concepts
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
Bivariate Data: observation on each of two variables
Multivariate Data: observations made on more than one variable
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
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Applied Statistics I
June 9, 2008
4 / 10
Basic Concepts
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.
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
Liang Zhang (UofU)
Applied Statistics I
June 9, 2008
5 / 10
Basic Concepts
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.
Descriptive Statistics: discipline of organizing and summarizing data
Inferential Statistics: discipline of drawing conclusions from a
sample to a population
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Applied Statistics I
June 9, 2008
6 / 10
Basic Concepts
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
Liang Zhang (UofU)
Applied Statistics I
June 9, 2008
7 / 10
Basic Concepts
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.
Liang Zhang (UofU)
Applied Statistics I
June 9, 2008
8 / 10
Probability & Statistics
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?
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?
Liang Zhang (UofU)
Applied Statistics I
June 9, 2008
9 / 10