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 BOXCHART Statement

## Percentile Definitions

You can use the PCTLDEF= option to specify one of five definitions for computing quantile statistics (percentiles). Let n equal the number of nonmissing values for a variable, and let x1, x2, ... ,xn represent the ordered values of the process variable. For the t th percentile, set p =t/100, and express np as
np = j + g
where j is the integer part of np, and g is the fractional part of np.

The t th percentile (call it y) can be defined in five ways, as described in the next five sections.

### PCTLDEF=1

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

### PCTLDEF=2

This uses the observation numbered closest to np
y=xi
where i is the integer part of np + 1/2.

### PCTLDEF=3

This uses the empirical distribution function

### PCTLDEF=4

This uses the weighted average aimed at xp(n+1)
y=(1-g)xj + gxj+1
where (n+1)p=j+g, and where xn+1 is taken to be xn.

### PCTLDEF=5

This uses the empirical distribution function with averaging

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