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.