Sampling from a non-Normally distributed population (CLT)
(0)This web visualization explores the sampling distribution of the mean when the data do not necessarily follow a Normal distribution.
Prerequisite Knowledge
- Familiarity with methods of summarizing data sets, such as mean and standard deviation
- The ability to recognize probability models as distributions with shape, centre, and spread
- The ability to recall the key properties of the Normal model
- The ability 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
Description
This web visualization is designed to be used after the students are familiar with the general principles of sampling. The Sampling from a Normal distribution visualization (linked under Related Resources) should be used first to introduce some of the basic concepts and the visual metaphors used here.
Code: https://www.zoology.ubc.ca/~whitlock/Kingfisher/
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.
Suggested Uses, Tips and Discoveries
These web visualizations 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, or other instructor-supplied material.
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. Read more.
Related Resources
Sampling from a Normal Distribution
This web visualization demonstrates the concept of a sampling distribution of an estimate, using the example of a mean of a Normally distributed variable. It also reinforces the idea of a histogram.
Creator
- Whitlock, Michael
Resource Type
Related Resource
Date Approved
Access
Everyone
https://statspace.elearning.ubc.ca/handle/123456789/76
Comments
Ratings in detail