It is common knowledge that average scores achieved by U.S. students on the Scholastic Aptitude Test (SAT) have been declining for years. It is less known that average SAT test scores among whites and blacks, Asians, Mexicans, and Puerto Ricans have generally risen over the past two decades. Average test scores have been declining while the "average" student is doing better. How can the overall average go down if subaverages for all of the constituent subgroups are going up? What has changed is not student performance, but demographics. Minority students, whose scores are rising the fastest, but from a lower base, are a rapidly growing part of the test pool. By focusing on the overall average rather than the averages of constituent subgroups, a picture of declining performance has been painted when performance has instead been improving. In business, the client of a major auditing firm encountered a similar problem. The company feared a loss in market share, as it noted a disturbing erosion in overall profit margins. Upon closer examination, the auditing firm found that profit margins were holding steady or rising in each product line, but that the product mix was changing in favor of lower margin products. As in the case of declining SAT scores, the "lie of averages" had emerged. Statistics such as overall averages do not lie, but they can be easily manipulated.1
Effective managers are adept at information processing made difficult by an environment that is complex and constantly changing. In this chapter, methods for characterizing the central tendency and dispersion of economic data are presented. This provides the background necessary for a more detailed examination of the statistical analysis of economic relations.
1 See Robert O'Brien, "Economic Data, Bargain Hunting Offset Fears About Accounting," The Wall Street Journal Online, February 20, 2002 (http://online.wsj.com).
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