The purpose of this handout is to summarize the meaning of information provided by a standard deviation regardless of the name given to the standard deviation and regardless of how it might be calculated. 
Given:

What you do

The Calculation

What the value estimates

Draw one sample of size n from a population  Calculate the standard deviation of the observations.
The sample standard deviation. 
The standard deviation of the population
"How much single observations jump around from one observation to the next." 
1. Draw one sample of size n from a population.
2. Calculation the standard deviation of the observations. 
Divide the standard deviation by
The standard error of the mean (SEM).

The standard error of the mean
"How much sample means jump around from one sample to the next." 
1. Draw r samples of size n from a population.
2. Calculate the sample mean for each sample. 
Calculate the standard deviation of the r sample means.
The standard deviation of the sample means. The standard error of the mean (SEM). There is no notation for this other than standard deviation. 
The standard error of the mean
"How much sample means jump around from one sample to the next." 
In the real world we would not know the population standard deviation and population meanall we would know is estimates calculated from samples. But since the samples on this page were generated via computerprogrammed Monte Carlo techniques we do. The population mean was 100 and the standard deviation was 10.
Three Problems

© 2002 by BurrtonWoodruff. All rights reserved. Modified