Chapter Contents Previous Next
 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 equals the number of nonmissing values for a variable and that x1, x2, ... ,xn represents the ordered values of the analysis variable. For the tth percentile, set p =t/100.

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

np = j + g
where j is the integer part of np, and g is the fractional part of np. For definition 4, let
(n+1)p=j+g

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

PCTLDEF=1
weighted average at xnp
y = (1 - g)xj + gxj+1
where x0 is taken to be x1

PCTLDEF=2
observation numbered closest to np
y = xi
where i is the integer part of np + 1/2 if . If g=1/2, then y=xj if j is even, or y=xj+1 if j is odd.

PCTLDEF=3
empirical distribution function
y = xj   if  g = 0
y = xj+1  if  g > 0

PCTLDEF=4
weighted average aimed at xp(n+1)
y=(1 - g)xj + gxj+1
where xn+1 is taken to be xn

PCTLDEF=5
empirical distribution function with averaging
y = (xj + xj+1)/2   if  g = 0
y = xj+1  if  g > 0

 Chapter Contents Previous Next Top