July 2002 
Vol. 4, No. 7 


Quality Quiz
from Professor Cleary
Congratulations!


Although he did not get caught by the
unsuspecting inspector, Hugh was wrong. Median charts offer a good
alternative to Xbar and R charts for two reasons. a) These can be done by hand, so for those with limited math skills, creating the charts is not an overwhelming task. b) By convention, a median chart shows not only the median value, but also the values of the observations. The real reason that control limits are about 25 percent wider than for Xbar and R charts deals with the difference in the way medians and averages are calculated. The mean uses all the data in a sample to estimate the central location of the population. The median orders the samples from smallest to largest and picks the middle number (assuming an odd sample size) as an estimate of central location of the population. With a sample size of 5, for example, all of the data would be used in calculating the mean, but only one number in calculating the median. It is as if the calculation of the median throws away the information in four of the five pieces of data. One would expect that the mean will be a more efficient estimator of central location of a population than would a median. (Note: An Ôefficient' estimator is one that is more precise in its ability to estimate a population parameter.) Statistician Walter Shewhart was aware of the phenomenon, and noted that the sampling distribution of sample medians will be about 25 percent more variable than the distribution of sample means.^{1} Poor Hugh N. Kry. He started out well, but because he was not willing to take time to investigate, he was wrong again. ^{1}Shewhart, W.A. Economic Control of Quality of Manufactured Product. New York, NY: D. Van Nostrand, 1931, pp. 18084.

Copyright 2002 PQ Systems.
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