Lecture 9 - Central Limit Thorem (CLT)

Introduction

• This is short asyncronous presentation about the Central Limit Theorem

• It includes

  • a few slides from my previous lectures

  • an excellent video made by another statistician

• This concept is relatively simple

• It will not be on Test 1, BUT…

  • it is an essential concept to know going forward.

What is the Central Limit Theorem (CLT)?

• The CLT is comprised a few related concepts (see video)

• For MAS 261 there is one primary concept you need to know:

  • Often times we are sampling from a population that does not have a normal (bell-shaped) distribution.

  • We also may have no way of knowing how the population is distributed.

  • The Central Limit Theorem states that:

    • If our sample size is large enough, then sampling distribution of the sample mean is NORMAL, even if the population distribution is not normal or is unknown.

    • A sample size of 30 more is sufficient no matter how the original population is distributed.

A Short (6 min.) Good Video About the CLT

I reviewed quite a few online resources to help explain the CLT.

This video by Dr. Nic of the Statistics Learning Center is Excellent.

• The Central Limit Theorem is comprised a few related concepts.

• The essential concept for this course going forward is this:

  • Regardless of the shape of the original population (ANY shape, really), the sampling distribution of the sample mean, \(\overline{X}\), is approximately normal IF our sample size is large enough (n=30).

• Because this material was provided asynchronously, you will have until Wednesday (9/27) at midnight to submit a question.