answered prayer, bell curves, ice cream, and commodes

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    Tyler wrote:
    > 7.  Half of the people in the world are below average.

    This is true only if the sample forms a perfectly symmetric curve.

    For example, let's take seven people Joe, Bob, Mary, Kay, Sue, Lee, and
    Bubba.  We'll measure their height in inches.

     Person   Height
     ------   ------
     Joe      70.0
     Bob      68.0
     Mary     62.0
     Kay      60.0
     Sue      65.0
     Lee      66.0
     Bubba    88.0

    The average height of these seven people is 68.4 inches.  Five out of
    the seven people sampled, or 71%, are "below average."

The problem here stems from the definition of "average".  You speak of
a perfect bell curve, which to me implies a Gaussian normal
distribution, yet you have a finite number of samples in your example,
and none can possibly be negative, and there is certainly an upper
bound also -- the tallest person in the sample space, so the normal
distribution is replaced by a binomial distr5ibution.  If you have an
infinite (or near infinite) number of samples, with a lower bound but
no upper bound (such as the speed of molecules in a gas), you would
use a Poisson distribution.  The computation of the first moment, or
mean (colloquialloy called the "average"), is no longer just the sum
of the samples divided by the number of samples.  Consult a good
college statistics text for the details...

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