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.

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

Learning Objectives

  • Identify and distinguish between a population and a sample, and between parameters and statistics
  • Interpret histograms for summarizing and comparing data sets
  • Explain the concepts of sampling variability and sampling distribution
  • Describe properties of the sampling distribution of the sample mean
  • Explain whether and how the population distribution and the sample size influence the sampling distribution of the sample mean from a Normal distribution


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. The sampling distribution is a complex concept. For instance, from our teaching, we have found that students often confuse the histogram of values from a random sample and the histogram of sample means from many random samples.  Read more.

Related Resources

Confidence intervals for the mean

This web visualization shows the meaning of a confidence interval, calculating confidence intervals of the means of repeated samples.

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.


  • Whitlock, Michael
Date Approved




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