# The BOXPLOT Procedure

### Percentile Definitions

You can use the PCTLDEF= option to specify one of five definitions for computing quantile statistics (percentiles). Suppose that n is the number of nonmissing values for a variable and that represent the ordered values of the analysis variable. For the tth percentile, set .

For the following definitions numbered 1, 2, 3, and 5, express as

where j is the integer part of , and g is the fractional part of . For definition 4, let

The tth percentile (call it y) can be defined as follows:

PCTLDEF=1

weighted average at

where is taken to be .

PCTLDEF=2

observation numbered closest to

where i is the integer part of if . If , then if j is even, or if j is odd.

PCTLDEF=3

empirical distribution function

PCTLDEF=4

weighted average aimed at

where is taken to be .

PCTLDEF=5

empirical distribution function with averaging