One of the four divisions of observations which have been grouped into four equal-sized sets based on their statistical rank. The quartile including the top statistically ranked members is called the first quartile and denoted . The other quartiles are similarly denoted , , and . For data points with of the form (for , 1, ...), the hinges are identical to the first and third quartiles.
The following table summarizes a number of common methods for computing the position of the first and third quartiles from a sample size (P. Stikker, pers. comm., Jan. 24, 2005). In the table, denotes the nearest integer function.
method | 1st quartile | 1st quartile | 3rd quartile | 3rd quartile |
odd | even | odd | even | |
Minitab | ||||
Tukey (Hoaglin et al. 1983) | ||||
Moore and McCabe (2002) | ||||
Mendenhall and Sincich (1995) | ||||
Freund and Perles (1987) |