Education Technology

Central Limit Theorem

Published on 10/05/2011

Activity Overview

This lesson involves examining distributions of sample means of random samples of size n from four different populations.

Objectives

  • Students will recognize that when n is sufficiently large, the sampling distribution of sample means, x̄, is approximately normal, regardless of the shape of the population distribution (Central Limit Theorem).
  • Students will recognize that when the population distribution is normal, the sampling distribution of sample means, x̄, is normal for any sample size n.
  • Students will recognize the consequences of the Central Limit Theorem when applied to quantitative data: a normal model with μ = μ (the true population mean) and that decreases as sample size, n, increases.
  • Students will recognize the consequences of the Central Limit Theorem when applied to proportions: a normal model with μ = P (the true population proportion) and σ that decreases as sample size, n, increases.

Vocabulary

  • Central Limit Theorem (CLT)
  • normal distribution
  • population
  • proportion
  • quantitative data
  • sample
  • sample mean
  • sample proportion
  • sampling distribution
  • skewed right distribution
  • spread
  • uniform distribution

About the Lesson

This lesson involves examining distributions of sample means of random samples of size n from four different populations.
As a result, students will:

  • Observe a uniform distribution and click to see simulated sampling distributions of size n=1 to 30 with a normal curve imposed on the distribution in each case.
  • Consider the same questions with respect to a normal distribution, a skewed distribution and a proportion.
  • Observe that as the sample size gets larger, the better the simulated sampling distribution can be approximated by a normal model.