Statistics: Central Limit Theorem

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_x̄ = 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_p̂ = P (the true population proportion) and σ_p̂ that decreases as sample size, n, increases.

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.