range vs. standard deviation

1. Go to http://www.aecouncil.com/data_analysis to get DE Histograms (free).
2. Click on “Give me some data in Excel”.
3.  Select some cells, and then click on “Normal Random Numbers Fill”.
4.  Find the range of your Sample from Step 3 (you can use Max()-Min()).
5.  Find the stdev() of the same Sample.
6.  Repeat.
7.  You will find that Rbar ~= stdev*d2.
d2(n) is listed in many statistics texts Appendices.
 

Range is a fact – the difference between largest and smallest values for a group of samples taken from a larger population (or, sometimes, the difference between consecutive samples).
Standard Deviation (for the samples) is also a fact (the ‘root mean square’ of deviations from the average value) but it’s really all about probability: a measure of the ‘likely’ deviation from the average. As other contributors have said, there is a shortcut for calculating it from successive range figures (as an alternative to the ‘rms’ method) but, whichever way it’s calculated, there’s an implicit assumption that the probability of a small deviation is greater than the probability of a large deviation. This is typically referred to as a NORMAL distribution, for which almost 100% (actually 99.7%) of samples would be expected to have a deviation of less than 3 x Std Dev. In other words, if you took 1000 samples you might expect to get 3 with a larger deviation than this (you might actually get more, or you might not get any!). Approx 68% would be expected to have a deviation less than the Std Dev.