The UNIVARIATE Procedure

Rounding

When you specify ROUND= $u$ , PROC UNIVARIATE rounds a variable by using the rounding unit to divide the number line into intervals with midpoints of the form $ui$ , where $u$ is the nonnegative rounding unit and $i$ is an integer. The interval width is $u$ . Any variable value that falls in an interval is rounded to the midpoint of that interval. A variable value that is midway between two midpoints, and is therefore on the boundary of two intervals, rounds to the even midpoint. Even midpoints occur when $i$ is an even integer $(0,\pm 2,\pm 4, \ldots )$ .

When ROUND=1 and the analysis variable values are between $-$ 2.5 and 2.5, the intervals are as follows:

Table 4.27: Intervals for Rounding When ROUND=1

$i$	Interval	Midpoint	Left endpt rounds to	Right endpt rounds to
$-$ 2	[ $-$ 2.5, $-$ 1.5]	$-$ 2	$-$ 2	$-$ 2
$-$ 1	[ $-$ 1.5, $-$ 0.5]	$-$ 1	$-$ 2	0
0	[ $-$ 0.5, 0.5]	0	0	0
1	[0.5, 1.5]	1	0	2
2	[1.5, 2.5]	2	2	2

When ROUND=0.5 and the analysis variable values are between $-$ 1.25 and 1.25, the intervals are as follows:

Table 4.28: Intervals for Rounding When ROUND=0.5

$i$	Interval	Midpoint	Left endpt rounds to	Right endpt rounds to
$-$ 2	[ $-$ 1.25, $-$ 0.75]	$-$ 1.0	$-$ 1	$-$ 1
$-$ 1	[ $-$ 0.75, $-$ 0.25]	$-$ 0.5	$-$ 1	0
0	[ $-$ 0.25, 0.25]	0.0	0	0
1	[0.25, 0.75]	0.5	0	1
2	[0.75, 1.25]	1.0	1	1

As the rounding unit increases, the interval width also increases. This reduces the number of unique values and decreases the amount of memory that PROC UNIVARIATE needs.