Percentiles

Percentile is in everyday use, but there is no universal definition for it. The most common definition of a percentile is a number where a certain percentage of scores fall below that number. You might know that you scored 67 out of 90 on a test. But that figure has no real meaning unless you know what percentile you fall into. If you know that your score is in the 90th percentile, that means you scored better than 90% of people who took the test.

In statistics, a percentile (or a centile) is a score below which a given percentage of scores in its frequency distribution fall (exclusive definition) or a score at or below which a given percentage fall (inclusive definition). For example, the 50th percentile (the median) is the score below which 50% (exclusive) or at or below which (inclusive) 50% of the scores in the distribution may be found.

The percentile (or percentile score) and the percentile rank are related terms. The percentile rank of a score is the percentage of scores in its distribution that are less than it, an exclusive definition, and one that can be expressed with a single, simple formula. In contrast, there is not one formula or algorithm for a percentile score but many. Hyndman and Fan identified nine and most statistical and spreadsheet software use one of the methods they describe. Algorithms either return the value of a score that exists in the set of scores (nearest-rank methods) or interpolate between existing scores and are either exclusive or inclusive.

• The 25th percentile is also called the first quartile.
• The 50th percentile is generally the median.
• The 75th percentile is also called the third quartile.
• The difference between the third and first quartiles is the interquartile range.