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# Chapter 1 descriptive_statistcs_1_2009_rev1_

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### Chapter 1 descriptive_statistcs_1_2009_rev1_

1. 1. CHAPTER 2 DESCRIPTIVE STATISTICS <ul><li>L1 – Numerical Summary of Data </li></ul><ul><li>L2 - Data Display and summary </li></ul>
2. 2. <ul><li>At the end of the lesson, students should be able to: </li></ul><ul><li>Explain the concepts of </li></ul><ul><ul><li>sample mean, population mean, </li></ul></ul><ul><ul><li>sample variance, population variance, sample standard deviation, </li></ul></ul><ul><li>Compute and interpret the sample mean, sample variance, </li></ul><ul><li>sample standard deviation, sample median, an sample range </li></ul>Learning Objectives:
3. 3. Population – Sample ( Definition) <ul><li>Population : </li></ul><ul><li>A collection, or set, of individuals or objects or events whose properties are to be analyzed. </li></ul><ul><li>( the number UTP students) </li></ul><ul><li>Sample : </li></ul><ul><li>A subset of the population. The number of individuals of a sample is called the sample size. </li></ul><ul><li>( the number of engineering students in UTP) </li></ul>
4. 4. Illustration of selection of a sample from a population
5. 5. Population - Sample <ul><li>Variable : </li></ul><ul><li>A characteristic of the objects in a population. </li></ul><ul><ul><li>CGPA of UTP students (number) </li></ul></ul><ul><ul><li>Gender of an engineering graduate ( category: male or female) </li></ul></ul><ul><li>Its value may change from one object to another in the population </li></ul><ul><li>Univariate : </li></ul><ul><li>A data set consists of observations on a single variable. </li></ul><ul><li>( type of transmission in a car, automatic or manual) </li></ul><ul><li>Multivariate : </li></ul><ul><li>A data set arises when observations made on more than one variable ( height and weight ) </li></ul>
6. 6. Variable Quantitative Qualitative or categorical (e.g. make of a computer, hair colour Gender) Discrete (e.g. number of houses, Cars, accidents Continuous (e.g. length, age, height, Weight, time) Types of variables
7. 7. Statistics Descriptive Statistics Inferential Statistics <ul><li>Methods of organizing, </li></ul><ul><li>display, and describe </li></ul><ul><li>important features of </li></ul><ul><li>data by </li></ul><ul><li>* tables, </li></ul><ul><li>* graphs, and </li></ul><ul><li>* summary measures </li></ul><ul><li>Methods that use sample </li></ul><ul><li>results to help make </li></ul><ul><li>decisions (inferences) or </li></ul><ul><li>predictions about a </li></ul><ul><li>population </li></ul>
8. 8. <ul><ul><li>The mean is the balance point for a system </li></ul></ul><ul><ul><li>of unit weights at points x 1 , x 2 , …,x n </li></ul></ul>Numerical Summary : Mean X 10 X 7 X 3 X 1 X 8 X 2 X 5 X 4 X 6 X 9 1.5 0 1 3 6.5 7 8.5 9.5 10 11 5.5
9. 9. Population mean (mu) : Sum of all values In the population The population size Sample mean The sample size Sum of all values In the sample MEAN
10. 10. Population variance : Population standard deviation is Numerical Summary : Variability
11. 11. <ul><li>Sample Variance </li></ul>Sample Standard Deviation : SD = s Numerical Summary : Variability