is the value of a variable below which a certain percent
of observations fall. So the 20th percentile is the value (or score) below which 20 percent of the observations may be found. The term percentile and the related term percentile rank
are often used in descriptive statistics
as well as in the reporting of scores from norm-referenced tests.
The 25th percentile is also known as the first quartile
); the 50th percentile as the median
or second quartile(Q2
); the 75th percentile as the third quartile (Q3
There is no standard definition of percentile
, however all definitions yield similar results when the number of observations is large. One definition, usually given in unsophisticated texts, is that the -th percentile of ordered values is obtained by first calculating the rank , rounding to the nearest integer, and taking the value that corresponds to that rank.
An alternative method, used in many applications, is to use linear interpolation between the two nearest ranks instead of rounding. Specifically, if we have values , , ,..., , ranked from least to greatest, define the percentile corresponding to the -th value as In this way, for example, if the percentile corresponding to the third value is
Suppose we now want to calculate the value corresponding to a percentile . If