adding the class width to the lowest data value. For the data in Table 2.2, the
first class interval is from 20.1 to (20.1 0.86), or 20.96. This class interval
includes all data from 20.1 up to (but not including) 20.96. The next class
interval is from 20.96 up to (20.96 0.86), or 21.82. Remaining class intervals
are found by adding the class width to the upper boundary value of the
preceding class. The class intervals for the data of Table 2.2 are listed in
column (1) of Table 2.3.
After creating class intervals, the number of data values in each interval,
called the class frequency, is tallied. Obviously, having data ordered consecutively
as shown in Table 2.2 aids greatly in this counting process. Column
(2) of Table 2.3 shows the class frequency for each class interval of the data
in Table 2.2.
Often, it is also useful to calculate the class relative frequency for each
interval. This is found by dividing the class frequency by the total number of
observations. For the data in Table 2.2, the class relative frequency for the
first class interval is 2/50 0.04. Similarly, the class relative frequency of
the fourth interval (from 22.67 to 23.53) is 13/50 0.26. The class relative
frequencies for the data of Table 2.2 are given in column (3) of Table 2.3.
Notice that the sum of all class relative frequencies is always 1. The class
relative frequency enables easy determination of percentages. For instance,
the class interval from 21.82 to 22.67 contains 16% (0.16 100%) of the
sample observations.
A histogram is a bar graph plotted with either class frequencies or relative
class frequencies on the ordinate, versus values of the class interval bounds
on the abscissa. Using the data from Table 2.3, the histogram shown in Figure
2.1 was constructed. Notice that in this figure, relative frequencies have been
plotted as ordinates.
Histograms drawn with the same ordinate and abscissa scales can be used
to compare two data sets. If one data set is more precise than the other, it
will have comparatively tall bars in the center of the histogram, with relatively