Standardized tests are administered in order to measure the aptitude or achievement of the people tested. A distribution of scores for all test takers allows individual test takers to see where their scores rank among others. Well-known examples of standardized tests include "IQ" (Intelligence Quota) tests, the PSAT (Preliminary Scholastic Achievement Test) and SAT (Scholastic Achievement Test) tests taken by high school students, the GRE (Graduate Requirements Examination) test taken by college students applying to graduate school, and the various admission tests required for business, law, and medical schools.

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...