STATISTICS IN SUMMARY

Chapter Specifics

image In Chapter 11, we discussed histograms and stemplots as graphical displays of the distribution of a single quantitative variable. We were interested in the shape, center, and variability of the distribution. In this chapter, we introduce numbers to describe the center and variability. For symmetric distributions, the mean and standard deviation are used to describe the center and variability. For distributions that are not roughly symmetric, we use the five-number summary to describe the center and variability.

In most of the examples, we used graphical displays and numbers to describe the distribution of data on a single quantitative variable. These data are typically a sample from some population. Thus, the numbers that describe features of the distribution are statistics, as discussed in Chapter 3. In the next chapter, we begin to think about distributions of populations. Thus, the numbers that describe features of these distributions are parameters. In later chapters, we will use statistics to draw conclusions, or make inferences, about parameters. Drawing conclusions about parameters that describe the center of a distribution of a single quantitative variable will be an important type of inference.

CASE STUDY EVALUATED Find the data on income by education at the Census Bureau website listed in the Notes and Data Sources section at the end of the book. Use what you have learned in this chapter to answer the following questions.

  1. 1. What are the median incomes for people 25 years old and over who are high school graduates only, have some college but no degree, have a bachelor’s degree, have a master’s degree, and have a doctoral degree? At the bottom of the table, you will find median earnings in dollars.

  2. 2. From the distribution given in the tables, can you find the (approximately) first and third quartiles?

  3. 3. Do people with more education earn more than people with less education? Discuss.

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image Online Resources

  • The StatClips Videos Summaries of Quantitative Data Example A, Example B, and Example C describe how to compute the mean, standard deviation, and median of data.

  • The StatClips Video Exploratory Pictures for Quantitative Data Example C describes how to construct boxplots.

  • The Snapshots Video Summarizing Quantitative Data discusses the mean, standard deviation, and median of data, as well as boxplots, in the context of a real example.