Use the diagrams on this page to help explain the difference between the standard deviation (of a sample) and the standard error (of a sample mean).

Theory

Use the slider to show that:

Standard deviation (SD)
Spread of values in the popn stays the same when n increases.
Standard error of the mean (SE)
Standard deviation of the sample mean, , decreases when n increases.

Simulation

This explains the same but using the sample SD and SE in simulated samples.


Make sure that students understand that:

Standard error does not describe the variability of individual values
A new value has about 95% probability of being within 2 standard deviations of sample mean.
Standard deviation does not describe the accuracy of the sample mean
The sample mean has about 95% probability of being within 2 standard errors of the population mean.