This edition: Sampling Distributions & the Central Limit Theorem
In this lesson, you will learn more about what investigators do with the numerical data they collect. You’ll see how statisticians use the average of values observed in samples to accurately determine the average in the population from which the sample was drawn. You will also learn about a theory that is central to all of statistics and which allows researchers to make approximations of population values based on a small sample of data. This lesson builds on what you learned about probability and random sampling to introduce a method that ascertains what will happen if a population is sampled many times. The result of this process, you’ll learn, is a new distribution derived from the samples. Statisticians analyze this new distribution to make precise estimations about the population under study. Once you understand this distribution, it opens the door into understanding the powerful theories behind statistics including the one (referred to above) that is central to the science of statistics. This lesson will show you how this central theory can reveal a great deal about a population based on the data from just a few samples. Mastering the concepts of the new distribution and this important theory will help you to understand the power of inference investigated in future lessons.