Pitt, Hy (1988, ASQC) Pitt Training Associates, Milwaukee, WI
The concept of standard deviation as a measure of variability is becoming more widely referred to in quality improvement programs that involve statistical process control (SPC) and other statistical applications. Although more people today than ever before have heard of standard deviation, only a relatively small portion of them use it on a regular basis, and shockingly much fewer (in fact, a rare number) really understand what it is. Hardly anyone can explain it properly.
Unfortunately, standard deviation is usually taught as a formula that one does not question or whose mathematical development is beyond the scope of such classes. Students are exhorted to plug in the numbers and grind out an answer. Even its relationship with the normal curve is unclear.
This paper attempts to remove the mystique usually associated with standard deviation by showing that the concept and the "mysterious" formula, that no one is supposed to understand, are the result of a logical sequence of common-sense idea that are simple and meaningful to all of us. It starts off with the idea that the mean (average) is used as a point of reference for determining variability in terms of distances (deviations) of readings from the mean. Then we try to determine the average of such distances as a way of comparing variabilities of one distribution from another. For example, we can decide, using this approach, if one process has more or less variability than other similar process. Because of stumbling blocks resulting from negative distances, we make sensible adjustments that evolve into the well-known formula for standard deviation, a logical result of common sense. From there insight is provided into its practical uses.
This method of presenting standard deviation has been used with great success with students from many different industries from all over the world. It differs considerably from the way it is formally taught in some universities and most industrial classes. The audience participates actively in the presentation and discussion.