Chapter 6: Distribution of the Sample Mean and the Central Limit Theorem

There are two types of statistics: descriptive and inferential. Chapters 1 and 2 focus on descriptive statistics; chapters 3, 4, and 5 are about probability (topics from these chapters will reappear in later chapters); chapters seven and all chapters after that will focus on inferential statistics. This chapter introduces the distribution of the sample mean and the central limit theorem, which provides a foundation for inferential statistics.

Learning Objectives

As a result of completing this chapter, you will be able to do the following:

  • Explain the difference between a statistic and a parameter.
  • Explain the relationships among a parameter, an estimator, and a point estimate.
  • Describe how to obtain the sampling distribution of the sample mean.
  • Explain and describe the distribution of sample mean in three aspects: mean, standard deviation, and shape.
  • Explain the central limit theorem in plain English.
  • Apply the central limit theorem to answer questions about the sample mean.


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