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Unformatted text preview: Chapter 12 Describing One Numerical Response 12.1 Study Suggestions Chapter 12 stresses the interpretation, rather than the construction and computation, of the visual presen- tation and numerical summaries of numerical data. The text suggests a variety of methods for data presentation. The dot plot provides the most faith- ful presentation of the data because it presents ex- act data values. Every other method groups data into class intervals. The rationale is that sometimes less detail gives a picture that is easier to interpret and understand. Remember that there is no universal sin- gle best way to present numerical data. Moreover, for any given set of data, different presentations may have different desirable features. In many situations it is necessary or desirable to have one or more numerical summaries of a set of data. The two popular measures of center are the mean and median. Resist the temptation to seek rules for deciding whether the mean or median is the bet- ter measure of center. Instead, it is important to un- derstand how the mean and median differ. Knowing the mean is equivalent to knowing the total, whereas knowing the median is not. Hence, if the total is im- portant, you probably will be unsatisfied with using the median alone as the measure or center. An ex- ample of the distinction is provided by a hypotheti- cal example of the salaries of professional athletes, for example, baseball players. A list of major league baseball players annual salaries for a given year will be skewed to the right with the mean substantially larger than the median. From the players point of view the median is a good measure of center because it represents the salary of a typical player; about one-half of the players earn more and about one-half of the players earn less than the median. The own- ers, however, are concerned with total salary outlay, so the mean is a good measure of center. (This argu- ment is simplified. At the time of this writing U.S. tax law provides tax breaks for employers of highly paid employees. As a result, the owners achieve a tax savings from having very expensive players. Thus, the real cost to an owner of players is a bit more com- plicated than the total of the salaries.) The value of the mean is sensitive to one or more outliers, but the median is not. Among the measures of spread, usually the in- terquartile range is matched with the median and the standard deviation is matched with the mean. The standard deviation is sensitive to outliers and the in- terquartile range is not. The standard deviation is very important for the theoretical developments of Chapters 13, 15, and 16, while the interquartile range has virtually no theoretical use....
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- Fall '09