PROC BOXPLOT: Percentile Definitions :: SAS/STAT(R) 9.22 User's Guide

The BOXPLOT Procedure

Percentile Definitions

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

For the following definitions numbered 1, 2, 3, and 5, express $\text{[math]}$ as

$\text{[math]}$

where $\text{[math]}$ is the integer part of $\text{[math]}$ , and $\text{[math]}$ is the fractional part of $\text{[math]}$ . For definition 4, let

$\text{[math]}$

The tth percentile (call it $\text{[math]}$ ) can be defined as follows:

PCTLDEF=1

weighted average at $\text{[math]}$

$\text{[math]}$

where $\text{[math]}$ is taken to be $\text{[math]}$ .

PCTLDEF=2

observation numbered closest to $\text{[math]}$

$\text{[math]}$

where $\text{[math]}$ is the integer part of $\text{[math]}$ if $\text{[math]}$ . If $\text{[math]}$ , then $\text{[math]}$ if $\text{[math]}$ is even, or $\text{[math]}$ if $\text{[math]}$ is odd.

PCTLDEF=3