Download Section 3: Measures of center

Probability and Statistics
Measures of center
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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 3: Measures of center
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Section 3: Measures of center
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Section 3: Measures of center
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Section 3: Measures of center
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Section 3: Measures of center
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Section 3: Measures of center
Example 0.8: The following data represent the number of
weeks it took seven individuals to obtain their driver’s
licenses. Find the sample median.
2, 110, 5, 7, 6, 7, 3
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Section 3: Measures of center
Solution: First arrange the data in increasing
order.
2, 3, 5, 6, 7, 7, 110
Since the sample size is 7, it follows that the
sample median is the fourth smallest value. That
is, the sample median number of weeks it took
to obtain a driver’s license is median = 6 weeks.
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Section 3: Measures of center
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Section 3: Measures of center
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Section 3: Measures of center
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Section 3: Measures of center
Definition (Sample mode): Mode is the value
which occurs most frequently. The mode may
not exist and even if it does, it may not be
unique.
Example 0.11: The following are the sizes of the
last 8 dresses sold at a women’s boutique:
10, 14, 12, 10, 4, 6 10, 8
What is the sample mode?
Solution: The sample mode is 10, since the value
of 10 occurs most frequently.
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Section 3: Measures of center
If no single value occurs most frequently, then all
the values that occur at the highest frequency are
called modal values. In such a situation we say that
there is no unique value of the sample mode.
Example 0.12: The ages of 6 children at a day care
center are
4, 2, 5, 3, 5, 2
What are the modal values of this data set?
Solution: Since the ages 2 and 5 both occur most
frequently, both 2 and 5 are modal values.
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Section 3: Measures of center
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Section 3: Measures of center
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