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Math 250

Math 250. Introduction to Probability and Statistics I. What is Statistics?. Statistics as a subject provides a body of principles and methodology for designing the process of data collection summarizing and interpreting the data drawing conclusions and generalities.

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Math 250

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  1. Math 250 Introduction to Probability and Statistics I

  2. What is Statistics? Statistics as a subject provides a body of principles and methodology for • designing the process of data collection • summarizing and interpreting the data • drawing conclusions and generalities.

  3. Figure 1.1 (p. 2)Gallup Opinion Index

  4. Statistics in our everyday life • Employment data • Consumer price index • Gallup poll • Quality and productivity improvement • Testing medicines

  5. Population and Sample A complete set of data is either physically impossible or from a practical standpoint not feasible (limitations of time, resources, facilities). • A unit is a single entity, usually a person or an object, whose characteristics are of interest. • The population of units is the complete collection of units about which information is sought. • A statistical population is the set of measurements (or record of some qualitative trait) corresponding to the entire collection of units. • A sample from a statistical population is the subset of measurements that are actually collected.

  6. Table 1.1 (p. 9)Populations, Units, and Variables

  7. How to select a sample? • Must be impartial and objective • Samples consisting of responses to call-in requests will, in general, not be representative of the population. • The name of each unit written on a separate slip of paper and the slips placed in a box; slips can be drawn one at a time without replacement • Using a random number table to select a sample

  8. Table 1.2 (p. 12)Random Digits: A Portion of Table 1, Appendix B

  9. Collection of Data Before collecting data • Develop a statement of purpose that is both specific and unambiguous. (e.g., is the water safe for swimming) • Translate the purpose into a measurement or a qualitative trait. (e.g., the amount of a radioactive material in water doesn’t exceed a certain safe limit)

  10. Objectives of Statistics The major objectives of statistics are: • To make inferences about a population from an analysis of information contained in sample data. This includes assessments of the extent of uncertainty involved in these inferences. • To design the process and the extent of sampling so that the observations form a basis for drawing valid inferences.

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