Variability Simulation

Learning Objectives

- State how changes in the mean and standard deviation affect the position and shape of the distribution.
- Identify differences in the means and standard deviations of distributions.

**Instructions**

The demonstration shows a graph of two normal distributions. Both distributions have means of 50. The red distribution has a standard deviation of 10; the blue distribution has a standard deviation of 5. You can see that the red distribution is more spread out than the blue distribution. Note that about two thirds of the area of the distributions is within one standard deviation of the mean. For the red distribution, this is between 40 and 60; for the blue distribution, this is between 45 and 55. About 95% of a normal distribution is within two standard deviations from the mean. For the red distribution, this is between 30 and 70; for the blue it is between 40 and 60.

You can change the means and standard deviations of the distributions and see the results visually. For some values, the distributions will be off the graph. For example, if you give a distribution a mean of 200, it will not be shown.

**Illustrated Instructions**

The demonstration starts with 2 normal distributions with equal means and different standard deviations (see screenshot below).

The means and standard deviations for both distributions can be changed and these changes will be reflected in the graph. The screenshot below shows the distributions with different means and standard deviations.

We recommend you answer the questions even if you have to guess. Then use the simulation to help you verify your answers. After interacting with the simulation click the "Check Answer" button.

Questions will appear here:

feedback

You can change the shape and location of the normal curves by changing their respective means and standard deviations.