Download Descriptive Statistics

Probability and Statistics
Fundamental Concepts
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Dr. Saeid Moloudzadeh
www.soran.edu.iq
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Contents
Descriptive Statistics
Axioms of Probability
Combinatorial Methods
Conditional Probability and
Independence
Distribution Functions and
Discrete Random Variables
Special Discrete Distributions
Continuous Random Variables
Special Continuous Distributions
Bivariate Distributions
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Probability and Statistics
Contents
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Descriptive Statistics
Axioms of Probability
Combinatorial Methods
Conditional Probability and Independence
Distribution Functions and Discrete Random Variables
Special Discrete Distributions
Continuous Random Variables
Special Continuous Distributions
Bivariate Distributions
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Chapter 0: Descriptive Statistics
0.1
0.2
0.3
0.4
Contents
Fundamental Concepts
Frequency table and graphs
Measures of center
Measures of variation
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Chapter 0: Descriptive Statistics
0.1
0.2
0.3
0.4
Contents
Fundamental Concepts
Frequency table and graphs
Measures of center
Measures of variation
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Section 1: Fundamental Concepts
Definition (Statistics): Statistics is the art of
learning from data. It is concerned with the
collection of data, their subsequent description and
their analysis, which often leads to the drawing of
conclusions.
There are two subdivisions of statistical method.
Definition (Descriptive Statistics): The part of
statistics concerned with the description and
summarization of data is called descriptive
statistics.
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Section 1: Fundamental Concepts
Definition (Inferential Statistics): The part of statistics
concerned with the drawing of conclusions from data is
called inferential statistics.
Definition (Population): The total collection of all the
elements (persons or things) that we are interested in is
called a population.
Definition (Sample): A subgroup of the population that
will be studied in detail is called a sample.
Definition (Random sample): A sample of k members of
a population is said to be a random sample, sometimes
called a simple random sample, if the members are
chosen in such a way that all possible choices of the k
members are equally likely.
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Section 1: Fundamental Concepts
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Section 1: Fundamental Concepts
Definition (Variable): A characteristic that varies from
one person or thing to another in population or sample is
called a variable.
Examples of variables for humans are height, weight,
number of siblings, sex, marital status, and eye color. The
first three of these variables yield numerical information
and are examples of quantitative variables, last three
yield non-numerical information and are examples of
qualitative (categorical) variables.
Observing the values of the variables for one or more
people or things yield data. This value may be a number,
a word, or a symbol. The collection of all observations for
particular variables is called a data set.
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Section 1: Fundamental Concepts
Qualitative and quantitative variables may be further subdivided:
Definition (Nominal Variable): A qualitative variable that
categorizes (or describes, or names) an element of a
population.
Definition (Ordinal Variable): A qualitative variable that
incorporates an ordered position, or ranking.
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Section 1: Fundamental Concepts
Definition (Discrete Variable): A quantitative variable
that can assume a countable number of values.
Intuitively, a discrete variable can assume values
corresponding to isolated points along a line interval.
That is, there is a gap between any two values.
Definition (Continuous Variable): A quantitative variable
that can assume an uncountable number of values.
Intuitively, a continuous variable can assume any value
along a line interval, including every possible value
between any two values.
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Section 1: Fundamental Concepts
Example 0.1: A college dean is interested in learning
about the average age of faculty. Identify the basic terms
in this situation.
The population is the age of all faculty members at the
college.
A sample is any subset of that population. For example,
we might select 10 faculty members and determine their
age.
The variable is the “age” of each faculty member.
One data would be the age of a specific faculty member.
The data would be the set of values in the sample.
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Section 1: Fundamental Concepts
Example 0.2: Identify each of the following examples as
qualitative or quantitative variables.
1. The residence hall for each student in a statistics class.
(Qualitative)
2. The amount of gasoline pumped by the next 10 customers at
the local Unimart. (Quantitative)
3. The amount of radon in the basement of each of 25 homes
in a new development. (Quantitative)
4. The color of the baseball cap worn by each of 20 students.
(Qualitative)
5. The length of time to complete a mathematics homework
assignment. (Quantitative)
6. The state in which each truck is registered when stopped
and inspected at a weigh station. (Qualitative)
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