The Sampling Distribution and Central Limit Theorem

by Douglas Brooks

The sampling distribution and Central Limit Theorem are the cornerstones of Statistics. Yet they are the hardest concepts for students to grasp. This booklet explains these concepts "In Plain English"(tm) so that they are easy to understand. Several examples are included for clarity.The sampling distribution is the distribution of all the possible means of all the possible samples of size n that can be taken from a population of size N. Brooks goes into detail explaining what that actually means! Then the Central Limit Theorem says that (for sufficient sample size --- again something that Brooks explains) the sampling distribution is a Normal curve with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. So what, you ask? Brooks explains that, also, and why it actually matters.It is hoped that the reader will obtain a really solid grasp of these two concepts, which will then make the study of the rest of Statistics much easier.Some understanding and/or exposure to basic measures of Statistics and probability will be helpful.The author has taught Statistics at the University level and has given seminars all over the world on technical topics. His specialty is making complex topics easy to understand for those without advanced college degrees.

31 pages, Kindle Edition

First published April 25, 2012