Quality Quiz from Professor Cleary

Our dauntless newly-appointed quality manager, Hartford Simsack, stumbled into the central limit theorem last month, with the help of Dr. Stan Deviation. While the concept seemed fascinating to him, it never occurred to him that it might be useful in understanding how control charts work. You will recall that he used Quality Gamebox to demonstrate the central limit theorem. Below, Gamebox illustrates data with two populations (left)--one with a single peak, and one with two peaks (a bimodal distribution). On the right, Gamebox has created two distributions made up of 1,000 samples of the size 1.

Gamebox creates two more distributions, this time with the means of 1,000 samples of size 2.

Finally, the Gamebox illustrates two more distributions, this time with the means of 1,000 samples of size 5.

These charts help to arrive at three conclusions about the distribution:

• The mean of the distribution is close to the mean of the population.
• The variability of that distribution is less than the population. (in fact, it is . )
• The shape is normal like.

Of course, Hartford Simsack sees all this, but still insists that the colorful graphs have nothing to do with control charts. How close is he to being right about this?

a) the charts are somewhat useful in understanding data, so they are remotely connected to control charts;

b) distribution, indeed, has nothing to do with control charts;

c) the central limit theorem is critical to control chart analysis.

Click here for a more complete video explanation

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