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Web Visualization: Sampling from a non-Normally distributed population (CLT)

This web visualization explores the sampling distribution of the mean when the data do not necessarily follow a Normal distribution.

This visualization is designed to be used after the students are familiar with the general principles of sampling. The Sampling from a Normal distribution visualization should be used first to introduce some of the basic concepts and the visual metaphors used here.

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Prerequisite Knowledge

Students should

be familiar with methods of summarizing data sets, such as mean and standard deviation;
be able to recognize probability models as distributions with shape, centre, and spread;
be able to recall the key properties of the Normal model;
be able to distinguish between a population and a sample, and between parameters and statistics.

Learning Objectives

Describe properties of the sampling distribution of the sample mean in general situations, using the Central Limit Theorem
For the sample mean, explain whether and how the population distribution and the sample size influence the sampling distribution of the sample mean

Suggested use(s) and tips

These resources are intended to be used in a number of ways,

as a visual aid during lectures;
as an open-ended learning tool for active learning;
as a guided learning experience, using either the built-in tutorials, guided activity sheet (click here for Instructor Guide and Activity Sheet), or other instructor-supplied material.

About this resource

Funding: University of British Columbia
Project Leader: Mike Whitlock
Programmers: Boris Dalstein, Mike Whitlock & Zahraa Almasslawi
Art: Derek Tan
Testing: Melissa Lee, Gaitri Yapa & Bruce Dunham
Thanks to: Darren Irwin, Dolph Schluter, Nancy Heckman, Kaylee Byers, Brandon Doty, Kim Gilbert, Sally Otto, Wilson Whitlock, Jeff Whitlock, Jeremy Draghi, Karon MacLean, Fred Cutler, Diana Whistler, Andrew Owen, Mike Marin, Leslie Burkholder, Eugenia Yu, Doug Bonn, Michael Scott, the UBC Physics Learning Group & the UBC Flex Stats initiative for numerous suggestions and improvements.

Related materials

"Making the most of demonstrations, videos, animations, or simulations in lectures and laboratories" (J. Maxwell and J. Stang)
It is recommended that the “Sampling from a Normal distribution” web visualization be used first to introduce some of the basic concepts and the visual metaphors used in the CLT web visualization: Web Visualization: Sampling from a Normal distribution
Video: Sampling Distribution of the Mean
Interactive Engagement Questions: Sampling distributions of means

What we learned

We learned a lot about this resource from trialling with students. Many students hold misconceptions related to the Central Limit Theorem. From our teaching, we have found that although students might be able to perform formal calculations, they often get confused with some of the concepts surrounding this topic.
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Web Visualization: Sampling from a Normal distribution

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• Sampling distributions - Sample mean
• Exploratory data analysis/Classifying data - Graphical representations - Histograms

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• Hypothesis tests - Goodness of fit - Chi-squared test for independence

Web Visualization: Confidence intervals for the mean

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