These 4 charts are 1000 random samples from a population of 9000 stocks. The population of 9,000 had a mean (mu) of 10% and a standard deviation (sigma) of 40%. Notice how they start to center at 10% almost immediately. Notice how the spread decreases with increasing sample size. Also note the general shape of the distributions -- kind of bell shaped?
The standard error can be estimated as the standard deviation of the means for each of the samples (i.e. 1000 samples) shown here.
There is also a theoretical formula for the standard error, please review the notes or the text for it.
