Chapter 3

# Chapter 3 - CHAPTER 3: SUMMARIZING & DESCRIBING DATA 3.1...

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3.1 DATA DESCRIPTION In the previous chapter, we discussed how to gather data intelligently for a designed experiment or an observational study, which is Step 2 in learning from data. We turn now to Step 3 , classification , summarizing , and presentation of the data . As already said in chapter 1, the field of statistics can be divided into two major branches: descriptive statistics and inferential statistics. In both branches, we work with a set of measurements. For situations in which data description is our major objective, the set of measurements available to us is frequently the entire population. For example, suppose that we wish to describe the distribution of annual incomes for all families registered in the 2000 census. Because all these data are recorded and are available on computer tapes, we do not need to obtain a random sample from the population; the complete set of measurements is at our disposal. Our major problem is in organizing , summarizing , and describing these data. That is, making sense of the data. Good descriptive statistics enable us to make sense of the data by reducing a large set of measurements to a few summary measures that provide a good, rough picture of the original measurements. In situations in which we are concerned with statistical inference, a sample is usually the only set of measurements available to us. We use information in the sample to draw conclusions about the population from which the sample was drawn. Of course, in the process of making inferences, we also need to organize , summarize , and describe the sample data. For example, a company is interested in determining the proportion of packages out of total production of a certain drug that are improperly sealed or have been damaged in transit. Obviously, it would be impossible to inspect all packages at all stores where the drug is sold, but a random sample of the production could be obtained, and the proportion defective in the sample could be used to estimate the actual proportion of improperly sealed or damaged packages. The objective of data description is to summarize the characteristics of a data set, identify any patterns in the data, and to present that information in a convenient form. When describing a distribution of data it is necessary to describe four things: ( 1 ) the center of the distribution, ( 2 ) the spread of the distribution, ( 3 ) the shape of the distribution, and ( 4 ) any unusual features in the distribution, such as extreme values ( outliers and influential points ), ranges of values not represented , and concentrations of data . In this chapter we will show how to construct charts, graphs, and tables that convey the nature of a data set. The procedure that we will use to accomplish this objective in a particular situation depends on the type of data, qualitative or quantitative, that we want to describe, and the number of variables measured. In this chapter we also present numerical

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## This note was uploaded on 04/15/2008 for the course QBA 2302 taught by Professor Dr.lohaka during the Spring '08 term at Baylor.

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Chapter 3 - CHAPTER 3: SUMMARIZING & DESCRIBING DATA 3.1...

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