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PAGE
FIVE
A Basic
Guide to Statistics
by Jonathan Dolhenty, Ph.D.
More
About the Normal Curve
As has been said, the normal curve concept is
very important in understanding the use of
statistics. Direct measures used in the behavioral
sciences, for instance, have been found to
approximate closely the mathematical model of the
normal distribution, which results in the
bell-shaped curve. Frequencies tend to concentrate
around the median and become fewer and fewer at
either end, resulting in a frequency curve which is
high in the middle and low at the ends.
In a perfect distribution, the mean, the median,
and the mode are located in the middle of the
bell-shaped curve. The mean, the median, and the
mode would have exactly the same value in a perfect
distribution.
Of course, this does not actually occur in the
real world when ordinary measurements are taken.
There are statistical procedures which help to
alleviate the problem of an imperfect match, but
these are for the professional statistician and
will not concern us here.
When positive or negative skewness does occur,
the mean, the median, and the mode will be located
in different places in the frequency distribution.
They will not match up as shown below.
The other bell curves shown below will give you
some information about what percentage of scores
will fall within certain ranges in a normal
distribution.
What
You Always Wanted to Know About I.Q
Scores
The frequency distribution for IQ scores is
shown below. A perfectly average IQ is 100, of
course, as indicated in the graph. This is also the
mean, the median, and the mode of the frequency
distribution.
Any score above 100 would technically be
considered "above average," and any score below 100
would technically be considered "below
average."
But, of course, considering statistical error
and so forth, such a designation in the "real"
world would be unfair and disingenuous. The
"average range" would be a more accurate
disignation. Most people fall into the "average
range." O.K.?
To Page 6
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