1. www.soran.edu.iq Probability and Statistics Dr. Saeid Moloudzadeh Measures of center 1 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

2. www.soran.edu.iq Probability and Statistics 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 2

3. www.soran.edu.iq Chapter 0: Descriptive Statistics Contents 0.1 Fundamental Concepts 0.2 Frequency table and graphs 0.3 Measures of center 0.4 Measures of variation 3

4. www.soran.edu.iq Chapter 0: Descriptive Statistics Contents 0.1 Fundamental Concepts 0.2 Frequency table and graphs 0.3 Measures of center 0.4 Measures of variation 4

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12. www.soran.edu.iq Section 3: Measures of center 12 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

13. www.soran.edu.iq 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. 13

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17. www.soran.edu.iq 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. 17

18. www.soran.edu.iq 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. 18

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