What the Standard Deviation Tells Us
Descriptive Statistical Techniques

Here are the same 400 observations but this time we've marked off a band showing values which range from 1 standard deviation below the mean to 1 standard deviation above the mean. If there were no sampling error, this band would include 68% of the observations. The box on the right increments each time an observation is within one standard deviation of the population mean.
These observations are a simulation of the results which would be obtained by measuring the height of young adult American women.
For this sample you will see that 281 of 400 observations fall within one standard deviation. That is an observed value of 70% of the cases rather than the the expected value of 68%. The sampling error in this instance is 2%.

Here's a movie illustrating a second sample of observations the proportion of observations which fall within 1, 2, and 3 standard deviations of the mean.

 These observations were created by simulating a normal population which describes the distribution of immediate memory span for digits. The population mean and standard deviation were set to values consistent with the research literature.
Remember

We expect 68% of the observations to be within one standard deviation; 96% within two SDs; and essentially all of the observations to be within 3 SDs of the mean.

Note how closely the observed proportions come to the values predicted from the normal curve model.

 And here are the results of another random sample from the same population.

 

 This is a second sample drawn from the population describing the distribution of immediate memory span for digits.

© 2002 by BurrtonWoodruff. All rights reserved. Modified Sunday, March 25, 2007