The UNIVARIATE Procedure

Rounding

When you specify ROUND= $\text{[math]}$ , PROC UNIVARIATE rounds a variable by using the rounding unit to divide the number line into intervals with midpoints of the form $\text{[math]}$ , where $\text{[math]}$ is the nonnegative rounding unit and $\text{[math]}$ is an integer. The interval width is $\text{[math]}$ . 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 $\text{[math]}$ is an even integer $\text{[math]}$ .

When ROUND=1 and the analysis variable values are between $\text{[math]}$ 2.5 and 2.5, the intervals are as follows:

Table 4.109 Intervals for Rounding When ROUND=1
$\text{[math]}$	Interval	Midpoint	Left endpt rounds to	Right endpt rounds to
$\text{[math]}$ 2	[ $\text{[math]}$ 2.5, $\text{[math]}$ 1.5]	$\text{[math]}$ 2	$\text{[math]}$ 2	$\text{[math]}$ 2
$\text{[math]}$ 1	[ $\text{[math]}$ 1.5, $\text{[math]}$ 0.5]	$\text{[math]}$ 1	$\text{[math]}$ 2	0
0	[ $\text{[math]}$ 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 $\text{[math]}$ 1.25 and 1.25, the intervals are as follows:

Table 4.110 Intervals for Rounding When ROUND=0.5
$\text{[math]}$	Interval	Midpoint	Left endpt rounds to	Right endpt rounds to
$\text{[math]}$ 2	[ $\text{[math]}$ 1.25, $\text{[math]}$ 0.75]	$\text{[math]}$ 1.0	$\text{[math]}$ 1	$\text{[math]}$ 1
$\text{[math]}$ 1	[ $\text{[math]}$ 0.75, $\text{[math]}$ 0.25]	$\text{[math]}$ 0.5	$\text{[math]}$ 1	0
0	[ $\text{[math]}$ 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.