Standard Deviation

     There arises an issue though when comparing two distributions which requires some additional insight.  For instance, if you examine the average corn price and its associated standard deviation over two different time periods, you may want to judge which period had the greatest variability.  Simply comparing the standard deviations would be the first thought, however, that would describe the absolute difference in variation. When comparing two different distributions we are usually interested in knowing their relative variability.

     One way is to compare the ratio of the standard deviations to the means.  This is a form of indexing and can reveal which variability is more significant (when compared to the average value).   Why is this important?  When I was a lot younger, I was a carpenter's assistant which meant that I would often have the job of cutting 2x4's to stated lengths called out by my boss.  At first, I was not very good at this and would often be off a small amount.  One day the boss was angry at me over this and told me the board I just cut was 1/2 inch off.  At first blush that sounded trivial to me so I told him 1/2 inch was not very much, and asked why was he so mad?  His reply was "if your nose was 1/2 inch longer you would think it was a big deal."

     Variation in a group or population is usually described with reference to one or more basic statistical functions.  The mean or average of a group or distribution is the most common statistic used.  It is calculated simply by adding all of the observations and dividing by the number of observations.  The mean is sometimes referred to as the expected value since it is a measure of central tendenancy and in one single oberservation, represents all of the different observations in the population.  All of the observations, when taken together, will be closer to the mean than any other single number.