Page 179 - Statistics for Dummies

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

hen you take a sample of data, it’s important to realize the results
Wwill 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 sam-
ples. 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 ran-
domly selected family has is a random variable. You use capital letters such
as X or Y to denote random variables and you use small case letters x or y

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