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Back to Everyone's Favorite Topic: Corn Prices

You can get an idea about some of the principles of variation by taking a look at everyone's favorite topic, corn prices. If you examine the average national corn price for the last ten years you will find that it was $2.28/bu with a standard deviation of about $0.43. Just by looking at those two numbers you can get an idea that there is some considerable variation going on in the historical pattern of corn prices.

Calculating the coefficient of variation (CV) yields 0.189, which you will recall is the standard deviation divided by the mean. Now if I were to ask you if the volatility in the corn market had increased since October 2006 what would your gut reaction be? I suspect you would be suckered in to saying "yes".

One Half Inch Doesn't Sound Like Much Unless Your Brain Surgeon is Off by That Amount

     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."

Management series: Managers not MBAs

Presentation from MIT OpenCourseWare on the topic of managers not MBAs.

Managers not MBAs. Click to listen or right click to download mp3 file to your computer.

If you prefer, this Flash based player will also play the audio. Double click play arrow.

Measuring Variation Or When You Think Rule of Thumb, Think and Thank Pafnuty

     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.

Management series: Leadership Lessons on the Firing Line

Presentation from MIT OpenCourseWare on the topic of leadership lessons on the firing line.

Leadership Lessons On The Firing Line. Click to listen or right click to download mp3 file to your computer.

If you prefer, this Flash based player will also play the audio. Double click play arrow.