## 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 *p*th percentile is a value, *Y*_{(p)},
such that at most (100*p*)% 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 75^{th} percentile in
height, and 50^{th} 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.

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