Statistics: Principles and Methods, 7th Edition

7

Variation in Repeated Samples—Sampling Distributions

1 The Sampling Distribution of a Statistic

2 Distribution of the Sample Mean and the Central Limit Theorem

Bowlers are well aware that their three-game averages are less variable than their single-game scores. Sample means always have less variability than individual observations.

Bowling Averages

A bowler records individual game scores and the average for a three-game series.

At the heart of statistics lies the ideas of inference. They enable the investigator to argue from the particular observations in a sample to the general case. These generalizations are founded on an understanding of the manner in which variation in the population is transmitted, by sampling, to variation in statistics like the sample mean. This key concept is the subject of this chapter.

Typically, we are interested in learning about some numerical feature of the population, such as the proportion possessing a stated characteristic, the mean and standard deviation of the population, or some other numerical measure of center or variability.

A numerical feature of a population is called a parameter.

The true value of a population parameter is an unknown constant. It can be correctly determined only by a complete study of the population. The concepts ...