Lecture Data ans statistics Applications in Business and Economics

1. Determine the number of nonoverlapping classes.
2. Determine the width of each class.
3. Determine the class limits.
Let us demonstrate these steps by developing a frequency distribution for the audit time data
in Table 2.4.
Number of classes Classes are formed by specifying ranges that will be used to group
the data. As a general guideline, we recommend using between 5 and 20 classes. For a small
number of data items, as few as five or six classes may be used to summarize the data. For
a larger number of data items, a larger number of classes is usually required. The goal is to
use enough classes to show the variation in the data, but not so many classes that some contain
only a few data items. Because the number of data items in Table 2.4 is relatively small
(n _ 20), we chose to develop a frequency distribution with five classes.
Width of the classes The second step in constructing a frequency distribution for quantitative
data is to choose a width for the classes. As a general guideline, we recommend that
the width be the same for each class. Thus the choices of the number of classes and the width
of classes are not independent decisions. A larger number of classes means a smaller class
width, and vice versa. To determine an approximate class width, we begin by identifying the
largest and smallest data values. Then, with the desired number of classes specified, we can
use the following expression to determine the approximate class width.
(2.2)
The approximate class width given by equation (2.2) can be rounded to a more convenient
value based on the preference of the person developing the frequency distribution. For example,
an approximate class width of 9.28 might be rounded to 10 simply because 10 is a
more convenient class width to use in presenting a frequency distribution.
For the data involving the year-end audit times, the largest data value is 33 and the
smallest data value is 12. Because we decided to summarize the data with five classes, using
equation (2.2) provides an approximate class width of (33 _ 12)/5 _ 4.2. We therefore
decided to round up and use a class width of five days in the frequency distribution.
In practice, the number of classes and the appropriate class width are determined by trial
and error. Once a possible number of classes is chosen, equation (2.2) is used to find the approximate
class width. The process can be repeated for a different number of classes. Ultimately,
the analyst uses judgment to determine the combination of the number of classes
and class width that provides the best frequency distribution for summarizing the data.
For the audit time data in Table 2.4, after deciding to use five classes, each with a width
of five days, the next task is to specify the class limits for each of the classes.