**Video Demo**

The attached script is useful for demonstrating the bias in estimating the population variance/standard deviation without using the corrected sample estimator (with n-1). This script can be used during lecture to demonstrate the concept, or can be given to students to use an an exploratory exercise.

Usage:

1. Run the attached script by pressing Control-R (on the PC), and Command-R (on the Mac).

2. Specify the population parameters, sample size, and number of sample to draw. (10k or more samples is recommended, and should take less than ~3 seconds on most computers)

3. The table of sample estimates will be generated, including:

- Sample Number
- Sample Size
- Sums of Squares for each sample
- Variance, estimated using the population form (with N in the denominator)
- Variance, estimated using the sample estimator form (with n-1 in the denominator)
- Standard Deviation, estimated using the population form (with N in the denominator)
- Standard Deviation, estimated using the sample estimator form (with n-1 in the denominator)

4. Run the saved scripts in the table to visualize and interact with the observed estimates. In the interface you can:

- Show the population variance/standard deviation on the histogram
- Show the observed mean estimate of the selected statistic

For ideas on using this script, see the **Video Demo** that I use in my course.

This script was developed in collaboration with mia.stephens. Please post any suggestions for future versions.

We hope this helps with your teaching!

julian