Computing the Quantiles (Percentiles) :: Base SAS(R) 9.4 Procedures Guide: High-Performance Procedures, Second Edition

Computing the Quantiles (Percentiles)

PROC HPBIN computes the 0% (minimum), 1%, 5%, 10%, 25%, 50%, 75%, 90%, 95%, 99%, and 100% (maximum) percentiles of each binning variable.

Let $m$ be the number of nonmissing values for a variable, and let $x_1$ , $x_2$ , ..., $x_ m$ represent the ordered values of the variable. Let the $t$ th percentile be $y$ , set $p = \frac{t}{100}$ , and let $mp$ = $j$ + $g$ , where $j$ is the integer part of $mp$ and $g$ is the fractional part of $mp$ . Then the $t$ th percentile is as described as:

$y = \begin{cases} x_ j & \text { if } g = 0 \\ x_{j+1} & \text { if } g > 0 \end{cases}$

Note: To avoid the time-consuming sorting process, the HPBIN procedure uses an iterative projection method to compute percentiles according to the preceding formula.

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The HPBIN Procedure

Computing the Quantiles (Percentiles)