December 2003  

Vol. 5, No. 12


Quality Quiz

Hartford Simsack, the intrepid quality manager from Greer Grate & Gate, has a limited understanding of “average” and has no intention of learning more. He is fond of using the expression “On average” to describe a variety of situations. If he has a week with several bad days and a couple of good days, he feels that “on average,” it's been a decent week, with no need to explore the concept further.

Dr. Stan Deviation, his statistics instructor at the community college as well as his unwitting mentor, has other ideas about averages. At first, Simsack does not understand why Dr. Stan “goes on and on” about averages, so during the lectures, he occupies himself with a solitaire game that he has installed on his Palm Pilot.

His attention is piqued, however, as Dr. Stan uses a simulation model in Quality GameBox to demonstrate how averages behave. Since Simsack is, on average, not winning with solitaire anyway, he perks up for the demonstration. Dr. Stan's model takes 1000 samples of various sizes from two populations. One is single peak distribution, the other a binomial distribution:

(Simsack's response to this is, “and that would be important because?”) The simulation model creates 1,000 random samples of the size one:

Not surprisingly, those samples create distributions that look similar to the distributions they came from. Simsack notices the contrast between the rather neat triangle represented by the “theoretical” and the ragged representation of actual data. Then Deviation hits the start button again and the simulation takes 1,000 samples of 2 each, then averages those samples and plots the averages from both distributions.

The histogram of the averages of samples of two is tighter and higher for the single peak distribution—a logical outcome since the sample size is 2 in this case.

Dr. Stan asks his class to explain why the bimodal distribution had become a tri-modal distribution. Simsack, fascinated by the colorful patterns that the data has created but not really engaged in the lesson, focuses intently on a spot on the floor beyond his desk to avoid eye contact with the professor.

If Dr. Stan were to call on you, what might you answer?

A) it can be explained by using the multiplication and addition probability rules;

B) unimodal is Step 1, bimodal is Step 2, Trimodal is Step 3;

C) Bimodal usually morphs into trimodal over time.


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