Percentile Definitions

You can use the PCTLDEF= option to specify one of five definitions for computing quantile statistics (percentiles). Suppose that 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 is the integer part of , and is the fractional part of . For definition 4, let


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


weighted average at


where is taken to be .


observation numbered closest to


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


empirical distribution function


weighted average aimed at


where is taken to be .


empirical distribution function with averaging