1.1 The Purpose of Statistics

Statistics are techniques used to summarize data in order to answer questions. Statistical techniques were developed because humans are limited information processors. Give a human a lot of numbers at once and that person will focus on just a handful of them—likely the most distinctive numbers, not the most typical ones. If Sara were applying to graduate school, would she want the admissions committee to see a list of grades (including the one D that will stick out like a sore thumb) or her GPA? In this case, GPA, which is a summary score—a statistic—is better than a hodgepodge of individual course grades.

Statistics bring order to chaos (Dodge, 2003). On the following three pages are some data from the Statistical Abstract of the United States, showing the percentage of the 18- to 25-year-old population, for each state, that has engaged in binge drinking at least once in the past 30 days. (Binge drinking is defined as five or more drinks within a couple of hours.) Table 1.1 is unorganized. It is hard to find a specific state, to figure out which state has the most/least binge drinking, or to figure out what the average is.

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Such a chaotic arrangement of data is not very useful. Just by alphabetizing the states, as in Table 1.2, order is brought to the data, making it easier to find a state.

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In Table 1.3, the binge drinking data are arranged from low to high, bringing a different order to the information. As a result, it is easy to see the range of binge drinking rates. This arrangement may bring up some questions: Care to speculate why Utah has the lowest rate? With the data sorted from low to high, it is even possible to get some sense of what the average score is.

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For another way to summarize the data, see Table 1.4. Here, the states are grouped into the four U.S. census regions (and within region from low to high), giving us some idea if geographic differences in binge drinking rates exist across the United States. All three tables (1.2, 1.3, and 1.4) arrange the data differently and answer different questions. Statistics involves organizing and summarizing information to answer a question.

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Practice Problems 1.1

Review Your Knowledge

1.01 What is the purpose of statistics?

Apply Your Knowledge

1.02 A researcher has collected IQ scores from a sample of sixth graders. What are some questions she might want to ask of the data? How would the data be arranged to answer the questions?