Basic Statistics

GRAPHS 41

showing the main features. In making a graph, we draw a picture of the situation,

and we may lose even more of the fine details. A well-done graph is usually easier to

read and interpret than the table.

Two ways of grafting a sample of continuous data are given here: the histogram

and the frequency polygon. In Section 5.5, some graphs are described that can be

used to display measures of the center and spread of a set of observations.

4.2.1 The Histogram: Equal Class Intervals

When the class intervals in the frequency distribution are equal, a histogram can be
drawn from it directly, using the frequencies, proportions, or percentages. Two lines,
one horizontal, the other vertical, are all that is needed; one line is called the horizontal
axis and the other, the vertical axis. A suitable scale is then marked on each axis.
The horizontal scale must be such that all the class intervals can be marked on it; it
need not begin at zero. The vertical scale should begin at the point where the axes
cross. If the histogram is to be plotted with frequencies, the scale must be chosen so
that all the frequencies can be plotted. With proportions or percentages, the vertical
scale must be chosen so that the largest one can be plotted.
After choosing the scale, class intervals are marked on the horizontal scale and
a vertical bar is erected over each class interval. The height of each bar is made to
equal the frequency, proportion, or percentage in that class.
Figure 4.1 shows two histograms drawn from the data in Table 4.5 for low-altitude
mine workers and relative frequencies computed for the high-altitude mine workers
using Table 4.4. Percentages are plotted on the vertical axis. In Figure 4.1, the numer-
ical values of the endpoints of the class intervals are marked on the horizontal axis.
Alternatively, many programs mark the midpoints of the class intervals so as to indi-
cate a typical value for that interval. Histograms may also be plotted using frequencies
on the vertical axis, but percentages are preferable for purposes of comparison when
the sample sizes are unequal.
In this example the histograms clearly show higher hemoglobin levels for the
high-altitude mine workers than for the low-altitude workers. Also, there is a greater
range between the highest and lowest values for the high-altitude workers. Almost
all statistical packages and many spreadsheet programs include procedures for mak-
ing histograms. Minitab, SAS, SPSS, and Stata all include the option of making
histograms.
For small sample sizes and for histograms not for publication, investigators some-
times draw quick histograms by placing an X in the appropriate class interval for each
observation. The result is a histogram of X’s instead of bars. This is used only for
actual frequencies. It is often drawn transposed with the class intervals on the vertical
axis, thus appearing somewhat like a stem and leaf graph.

4.2.2 The Histogram: Unequal Class Intervals

When drawing a histogram from a set of data with unequal class intervals, we must

first adjust for the length of the class intervals in order to avoid a graph that gives a