*Macmillan Science Library: Mathematics*. Copyright © 2001-2006 by Macmillan Reference USA, an imprint of the Gale Group. All rights reserved.

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## The "Normal" Curve

The mathematics behind the distribution of scores on standardized tests comes from the fields of probability theory and mathematical statistics. A cornerstone of this mathematical theory is the "Central Limit Theorem," which states that for large samples of observations (or scores in the case of standardized tests), the distribution of the observations will follow the bell-shaped normal probability curve illustrated below. This means that most of the observations will cluster symmetrically around the mean or average value of all the observations, with fewer observations farther away from the **mean** value.

One measure of the spread or dispersion of the observations is called the **standard deviation**. According to statistical theory illustrated above, about 68 percent of all observations will lie within plus or minus one standard deviation of the mean; 95 percent will lie within plus or minus two standard deviations of the mean (see graph below...

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