The percentile rank of a score is the percentage of scores in its frequency distribution which are lower. For example, a test score which is greater than 90% of the scores of people taking the test is said to be at the 90th percentile. In statistics, a frequency distribution is a list of the values that a variable takes in a sample. ...

Percentile ranks are commonly used to clarify the interpretation of scores on standardized tests. For the test theory, the percentile rank of a raw score is interpreted as the percentages of examinees in the norm group who scored below the score of interest (Crocker & Algina, 1986). The mathematical formula is Originally a standardized test was simply a standard test – of academic achievement or of knowledge in a specific academic or vocational domain. ...

where cf_l is the cumulative frequency for all scores lower than the score of interest, f_i is the frequency of the score of interest, and N is the number of examinees in the sample. If the distribution is normally distributed, the percentile rank can be inferred from the standard score. The normal distribution, also called Gaussian distribution, is an extremely important probability distribution in many fields. ... Compares the various grading methods in a normal distribution. ...

Unlike a normal distribution of scores, which are bell shaped, the distribution of percentile ranks is uniform and is rectangular in shape.

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Reference:

Crocker, L., & Algina, J. (1986). Introduction to classical and modern test theory. New York: Harcourt Brace Jovanovich College Publishers.