- The vertical scale represents the frequency or relative frequency in each
interval (see the exceptions below).
A histogram presents us with a graphic picture of the distribution of mea-
surements. This picture consists of rectangular bars joining each other, one for
each interval, as shown in Figure 2.2 for the data set of Example 2.2. If disjoint
intervals are used, such as in Table 2.2, the horizontal axis is marked with true
boundaries. Atrue boundaryis the average of the upper limit of one interval
and the lower limit of the next-higher interval. For example, 19.5 serves as the
true upper boundary of the first interval and the true lower boundary for the
second interval. In cases where we need to compare the shapes of the histo-
grams representing di¤erent data sets, or if intervals are of unequal widths, the
height of each rectangular bar should represent the density of the interval,
where the interval density is defined by
density¼
relative frequencyð%Þ
interval widthThe unit for density ispercent per unit(of measurement): for example, per-
cent per year. If we graph densities on the vertical axis, the relative frequency is
represented by the area of the rectangular bar, and the total area under the
histogram is 100%. It may always be a good practice to graph densities on the
vertical axis with or without having equal class width; when class widths are
Figure 2.2 Distribution of weights of 57 children.TABULAR AND GRAPHICAL METHODS 63