A hand in the tilde:
Polly Yurrathane Tries Median Ground
Quality manager Polly Yurrathane is in deep trouble. Her boss, Hammond Eggs, has been ranting for days about the diminishing quality of the company’s products. The firm, which manufactures a variety of toy products, has undergone scrutiny by a major consumer journal; in addition, stores are complaining about high rates of return for the toys that Play With Us, Inc., manufactures.
Hammond Eggs orders Polly to hire “as many inspectors as we need” to keep defective products from going off the assembly line and being shipped to stores. Polly, who rarely responds to her boss in anything but a meek “Yes, sir,” summons the courage to point out that a system of prevention is always preferable to one of detection. “I hired you to prevent mistakes,” the boss shouts. “And that hasn’t worked, so we’ll inspect every blasted toy that we make,” ordering Polly to hire ten inspectors immediately, at minimum wage. (The local fast food store, it should be noted, is currently paying $9.50 per hour and still has a ”Help Wanted” sign in its window.)
Knowing that she must find inspectors immediately, Polly goes to the local unemployment office and pleads with people in line, finally attracting ten who say they will show up on Monday. Although only eight workers actually appear on schedule, Polly is undaunted, and decides to teach them about X-bar and R charts on the first day. The training room is set, with calculators at each station, and she begins to lecture. These new students do well with the concept of range:
They have a hard time calculating averages, however, in spite of Polly’s use of batting averages as a model for the calculations. They seem to be totally puzzled by the statistical symbols:
She suddenly recalls the use of median charts, where only the median is recorded, rather than the mean, popularized by Dr. Paul Clifford after World War II. Common practice called for sample sizes of 3 or 5, so no math was necessary. For example:
Data: 14, 12, 17, 19, 15
Median: 12, 14, 15, 17, 19
To calculate the median, the data must be ordered from the smallest to the largest number; the middle number is the median. In this example, it would be 15.
Excited by this approach, Polly teaches her motley crew how to do median charts, beginning with the following formula that she writes on the whiteboard:
Unfortunately for her, one of the new hirees had been employed previously as an inspector. Just as Polly Yurrathane finishes her brilliant lesson, this inspector asks why the A 2 factor is different for median charts than for X-bar and R charts. He has used his calculator to figure that the A 2 factor for median charts, called A 2 tilde (~) is about 25 percent larger than the A 2 for X-bar and R charts.
Polly, flushed from her spectacular performance in teaching median charts, now finds herself at a loss. Not wanting to embarrass herself by admitting that she does not know, she points out that the square root of .0625 is equal to .25. The old inspector accepts this answer, since he himself is not adept at math.
Is Polly Yurrathane’s response appropriate?
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