Quantiles
It is often convenient to subdivide the area under a density
curve so that the area to the left of the dividing value
is some specified fraction of the total unit area.
For a given value of p between 0 and 1,
the pth quantile (or 100 pth percentile)
is the value such that the area to the left of it is p.
The pth quantile is computed from
the empirical distribution function with averaging:
where i is the integer part and f is the
fractional part of np=i+f.
If you specify a Weight variable, the pth quantile is computed as
When each observation has an identical weight, the weighted quantiles
are identical to the unweighted quantiles.
The Quantiles table, as shown in Figure 38.9,
includes the following statistics:
- 100% Max is the maximum, y_{(n)}.
- 75% Q3 is the upper quartile (the 75th percentile).
- 50% Med is the median.
- 25% Q1 is the lower quartile (the 25th percentile).
- 0% Min is the minimum, y_{(1)}.
- 99%, 97.5%, 95%, 90%, 10%, 5%, 2.5%, and 1%
give the corresponding percentiles.
- Range is the range,
y_{(n)} - y_{(1)}.
- Q3-Q1, the interquartile range, is the
difference between the upper and lower quartiles.
- Mode is the most frequently occurring value.
When there is more than one mode, the lowest mode is displayed.
When all the distinct values have frequency one, the value is
set to missing.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.