**EVERYBODY
HAS HEARD OF BIGFOOT, THE MYSTICAL FIGURE THAT LIVES IN THE WOODS, BUT
NOBODY HAS EVER** actually seen him. Similarly,
there are some concepts from basic statistics that everybody has heard
of but that—like Bigfoot—always remain a little shrouded in mystery.
Here, we take a look at three of them: the average of averages, the
mystical standard deviation, and the ever-popular least squares.

Recently, someone approached me with the following question:
given the numbers in Table 11-1, what number
should be entered in the lower-right corner? Just adding up the
individual defect rates per item and dividing by 3 (in effect,
averaging them) did not seem right—if only because it would come out
to about 0.75, which is pretty high when one considers that
*most* of the units produced (100 out of 103) are
not actually defective. The specific question asked was: “Should I
weight the individual rates somehow?”

This situation comes up frequently but is not always recognized:
we have a set of rates (or averages) and would like to summarize them
into an overall rate (or overall average). The problem is that the naive way of doing so (namely, to
add up the individual rates and then to divide by the number of rates)
will give an *incorrect* result. However, this is
rarely noticed unless the numbers involved are as extreme as in the
present example.

Table 11-1. Defect rates: what value should go into the ...

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