Key Concepts About Percentiles
The rank or percentile rank of a raw score is the percentage of individuals in the distribution with scores at or below that particular score. When a raw score is identified by its percentile rank, the score is called a percentile. Using mathematical terms, the pth percentile is a value, Y(p), such that at most (100p)% of the measurements are less than this value and at most 100(1- p)% are greater.
Percentiles are useful because raw scores, or X values, do not provide enough information by themselves. For example, if you are told that a boy is 27 inches tall and weighs 30 pounds, you may not be able to tell how well the boy is doing. You need additional information such as the average score of his age group, or the number of boys who score above or below this boy in his group. To determine the relative position of the boy's measurements in his group, you need to transform the raw scores into percentiles in order to compare. Therefore, it is much more informative if you could transform the height and weight of the boy into percentile rank, such as 75th percentile in height, and 50th percentile in weight in his age group.
In summary, percentiles provide additional information about the distribution of values. percentiles represent the relative position of the measured values within a distribution.
