Quality Quiz from Professor Cleary
"B" is correct.
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Although she did not get caught by the unsuspecting inspector, Polly was wrong. Median charts offer a good alternative to X-bar 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 plots the values of the remaining observations.
An example of a median chart for Hammond Eggs’ data:
The real reason that control limits are about 25 percent wider than for X-bar 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, all data values are used in calculation of the mean but only one number is used to determine the value of 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 would be a more efficient estimator of central location of a population than would a median (Note: An “efficient” 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 Polly Yurrathane. She started out well, but her ego would not allow her to take the time to investigate and find out the right answer.
1 Shewhart, W.A. Economic Control of Quality of Manufactured Product. New York: D. Van Nostrand, 1931. Pg. 278.
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