noninclusive. For example, if the variable AGEY had a value of 18.5 then this value
could be part of the first class interval, 16.5 to 18.5, or part of the second class interval
18.5 to 20.5. SAS would automatically include the first occurrence of 18.5 (in the first
class interval) and exclude the second occurrence of 18.5 (from the second class interval).
Sometimes it is useful to calculate the mid-point of a class interval as this may be
used to plot frequency histograms. This is the exact centre of the interval, that is half way
between an interval’s real limits. The mid-point of an interval can be calculated by
adding half of the size of the class interval to the lower real limit of the interval. The mid-
point of the lowest interval, 17–18, in Table 3.4 is (18.5−16.5)/2+16.5=17.5.
HistogramA histogram is similar in some respects to a bar chart, it has bars which represent the
relative values of a variable. However, it is unlike a bar chart in three important ways.
The horizontal scale is continuous, in a bar chart it is discrete. The width of a bar or block
in a histogram, unlike in a bar chart, is important for interpretation. In a histogram the
bars are usually of constant width representing equal intervals on the continuous scale. A
bar chart usually has a bar width of unity but this has no interpretative meaning. It is
actually the area in each histogram bar that is crucial for interpretation. The area is clearly
related to the width of each bar. The height of a bar in a histogram may represent either a
frequency or a percentage.
Example 3.9Figure 3.15 shows a histogram for the variable age in years (AGEY) from the A-level
data set.
Initial data analysis 61