# Chapter 11

# Sampling Distributions and the Central Limit Theorem

*In This Chapter*

- Understanding the concept of a sampling distribution
- Putting the Central Limit Theorem to work
- Determining the factors that affect precision

**W**hen you take a sample of data, it's important to realize the results will vary from sample to sample. Statistical results based on samples should include a measure of how much those results are expected to vary. When the media reports statistics like the average price of a gallon of gas in the U.S. or the percentage of homes on the market that were sold over the last month, you know they didn't sample every possible gas station or every possible home sold. The question is, how much would their results change if another sample was selected?

This chapter addresses this question by studying the behavior of means for all possible samples, and the behavior of proportions from all possible samples. By studying the behavior of all possible samples, you can gauge where your sample results fall and understand what it means when your sample results fall outside of certain expectations.

*Defining a Sampling Distribution*

A *random variable* is a characteristic of interest that takes on certain values in a random manner. For example, the number of red lights you hit on the way to work or school is a random variable; the number of children a randomly selected family has is a random variable. You use capital letters such as *X* or *Y* to denote random variables and you use small ...