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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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