August 2001 Vol. 3, No. 8
Quality Quiz from Dr. Cleary

Congratulations!
You're right!

A sample size of 5 allows for a shortcut to calculate the average. Five is the conventional sample size, not because of its link to any statistical principle, but because, as statistician Walter Shewhart pointed out, it makes calculations more convenient.

The use of a sample size of 5 came about because it allowed for an easy way to calculate the mean.

 For example:

 Sample 12, 14, 10, 12, 15:

Shortcut Method:

 By taking the sum of the samples, multiply by 2, and move the decimal point one place to the left, the same result is generated: 12 + 14 + 10 + 12 + 15 = 63 63 x 2 = 126 By moving the decimal point one place to the left, we derive 12.6

The control chart, remember, was developed in the 1930's before the ten-dollar calculator or the PC were available for statistical calculations.

By the way, don't confuse your kids by announcing this "new" way to calculate the average. This method works only if the sample size is 5.

* Shewhart, W.A., Economic Control of Quality of Manufactured Product (New Jersey: VanNorstrand Reinhold Company, Inc., 1931)

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