Calculating Percentiles
The UNIVARIATE procedure automatically computes the 1st, 5th, 10th, 25th, 50th,
75th, 90th, 95th, and 99th percentiles (quantiles), as well as the minimum and maximum
of each analysis variable. To compute percentiles other than these default percentiles, use
the PCTLPTS= and PCTLPRE= options in the OUTPUT statement.
You can specify one of five definitions for computing the percentiles with the
PCTLDEF= option. Let be the number of nonmissing values for a variable, and let
represent the ordered values of the variable. Let the th percentile be , set
, and let
where is the integer part of np, and is the fractional part of np. Then the PCTLDEF=
option defines the th percentile, , as described in the Table 4.83.
PCTLDEF
Description
1
weighted average at
Formula
where
2
observation numbered closest to np
3
empirical distribution function
4
weighted average aimed
at
5
empirical distribution function with averaging
where
is taken to be
is taken to be