A More Relaxed Rule for the Real World

You may feel that it is a little odd to say 'about 99.7%', after all, 99.7% is a rather precise figure. The figures for the empirical rule were obtained using integral calculus to work out the area under a theoretical normal curve. Such a curve does not exist anywhere except as an abstract mathematical concept. Therefore, when dealing with real world data, it is advisable to be less precise about what may be expected. This is especially important because one cannot assume that data in the real world are normally distributed. Finally, when dealing with control chart data we are not dealing with the standard deviation per se, rather, we are dealing with sigma units.

In light of this, it is reasonable to expect to find:

• about 60% - 75% within 1 sigma unit of the mean
  
  
• about 90% - 98% within 2 sigma units of the mean
  
  
• about 99% - 100% within 3 sigma units of the mean

These more relaxed ranges are far more appropriate for real world data, and the third part is very reliable even when the data are not normally distributed. However, even given the broad range of expected values for the first two parts, this is still only a guide, not an absolute, hard and fast rule.