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Using an Applet to Demonstrate a Sampling Distribution

This page authored by Roger Woodard, Jennifer Gratton, Steve Stanislav, and Pam Arroway, North Carolina State University, based on an applet by David Lane, Rice University.
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This activity has been undergone anonymous peer review.

This activity was anonymously reviewed by educators with appropriate statistics background according to the CAUSE review criteria for its pedagogic collection.

This page first made public: May 9, 2007

This material was originally developed through CAUSE
as part of its collaboration with the SERC Pedagogic Service.


This in-class demonstration combines real world data collection with the use of the applet to enhance the understanding of sampling distribution. Students will work in groups to determine the average date of their 30 coins. In turn, they will report their mean to the instructor, who will record these. The instructor can then create a histogram based on their sample means and explain that they have created a sampling distribution. Afterwards, the applet can be used to demonstrate properties of the sampling distribution. The idea here is that students will remember what they physically did to create the histogram and, therefore, have a better understanding of sampling distributions.

Learning Goals

Context for Use

This demonstration can be used as a first introduction to the concept of sampling distributions. It has been applied at the undergraduate level, but could also be used at the advanced placement level as well. Including the time spent for viewing the applet, this activity can be completed in a 50 minute class period.

Prior to this activity students should be able to calculate the mean and should have seen distributions of many different shapes.

Teaching Materials

In this activity students are exposed to the concept of sampling distributions by creating a sampling distribution as a class. By having the students assemble a sampling distribution, they can more readily understand that a sampling distribution is made up of a collection of sample statistics from different samples. Materials Needed

Teaching Notes and Tips

This demonstration is appropriate for classes as small as 20 students to those large as 200 students. In either, case you want to have at least 20 samples of 30 coins. For small class sizes students should work on individually. For a large class size, break students into groups of up to 3.

Careful planning will make this demonstration go smoothly. Some specific tips include:


This concept is very deep and can be assessed on several levels. Students can be given a scenario and asked to describe the sampling distribution. Students should also be prompted to explain what makes up the sampling distribution. At the most basic level students should be able to choose a histogram that reflects the sampling distribution of a sample mean. An example of such a question can be found in the file: Sampling distribution questions. (Microsoft Word 201kB May2 07)

References and Resources


Mathematics, Statistics:Statistical Inference and Techniques:Sampling Distributions, Mathematics:Statistics:Statistical Inference and Techniques, Mathematics:Statistics, Statistics:Data Collection

Resource Type


Grade Level

High School (9-12), College Lower (13-14):Introductory Level, College Lower (13-14)

Ready for Use

Ready to Use:Meets Peer Review Standard:Anonymous Peer Review

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