STATISTICS IN SUMMARY

Chapter Specifics

image Chapters 10, 11, and 12 provided us with a strategy for exploring data on a single quantitative variable.

In this chapter, we added another step: sometimes the overall pattern of a large number of observations is so regular that we can describe it by a smooth density curve, such as the Normal curve. This step also allows us to identify “a large number of observations” as a population and use density curves to describe the distribution of a population. We did precisely this when we used the Normal distribution to describe the distribution of the heights of all young women or the scores of all students on the SAT exam.

Using a density curve to describe the distribution of a population is a convenient summary, allowing us to determine percentiles of the distribution without having to see a list of all the values in the population. It also suggests the nature of the conclusions we might draw about a single quantitative variable. Use statistics that describe the distribution of the sample to draw conclusions about parameters that describe the distribution of a population. We will explore this in future chapters.

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CASE STUDY EVALUATED The Normal curve that best approximates the distribution of body temperatures in Figure 13.2 and 13.3 has mean 98.25°F and standard deviation 0.73°F. Use what you have learned in this chapter to answer the following questions.

  1. 1. According to the 68–95–99.7 rule, 68% of body temperatures fall between what two values? Between what two values do 95% of body temperatures fall?

  2. 2. There was a time when 98.6°F was considered the average body temperature. Given what you know about the distribution of body temperatures given in Figure 13.2 and 13.3, what percentage of individuals would you expect to have body temperatures greater than 98.6°F? What percentage would you expect to have body temperature less than 98.6°F?

image Online Resources

  • LearningCurve has good questions to check your understanding of the concepts.