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He’s wrong. It is too good to be true.

January’s quiz demonstrated how the averages of samples of 5 behave. That is, if many averages are taken from samples of the size of 5 and a histogram is created from these averages, the shape of the histogram (or distribution) would be normal. But looking at Perry Winkel’s chart, one would expect about 68 percent of the X-bars to lie between plus and minus one (1) sigma ( ). But Perry Winkel’s chart shows that 100 percent of the X-bars are between plus and minus one sigma (). This is, of course, statistically impossible. Given the natural variability of averages, one would expect only 68 percent, never 100 percent.

Like myself, you have perhaps seen the same kind of “perfect” chart. The most common explanation for this is that whoever is generating the charts believes that a boss will be pleased to see averages (X-bars) close to the mean of the average ( ). This sometimes results in editing data, so that what is on the chart may have nothing to do with actual readings. Some call this “the broken pencil approach.”

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