Quantitative data can be presented in the form of frequency distribution tables. Here is a typical frequency distribution table (FDT).
Table 1 shows the duration of 20 conversations. There are five classes (or categories) for the duration. Each class is assigned to a symbol called class interval. The class interval of the first class is 5 – 9 minutes, the class interval of the second class is 10 – 14 minutes, etc. The frequencies in the table indicate how many conversations fall in each category/class. For example, there are 3 conversations whose duration is between 5 and 9 minutes, 5 conversations whose duration is between 10 and 14 minutes, etc.
Class Limits
There are five classes in Table 1. Each class has a lower class limit (LCL) and an upper class limit (UCL). LCL of class #1 is 5 minutes and the UCL is 9 minutes. LCL of class #2 is 10 minutes and the UCL is 14 minutes, etc.
Class Boundaries
Each class has a lower class boundary (LCB) and an upper class boundary (UCB). If the data in the FDT are presented in whole numbers, then LCB = LCL – 0.5 and UCB = UCL + 0.5. For example, in class #1, LCB = (5 – 0.5) minutes = 4.5 minutes and UCB = (9 + 0.5) minutes = 9.5 minutes. The following is the list of the class boundaries of each class.
But if the class limits are accurate to 1 decimal place, LCB = LCL – 0.05 and UCB = UCL + 0.05. For instance, in the table below, the LCB of class #1 is 5.0 – 0.05 = 4.95 and the UCB is 9.9 + 0.05 = 9.95.
In class #2, LCB = 10.0 – 0.05 = 9.95 and UCB = 14.9 + 0.05 = 14.95. In class #3, LCB = 15.0 – 0.05 = 14.95 and UCB = 19.9 + 0.05 = 19.95, etc. The following table summarizes the class boundaries of each class.
As Table 4 shows, the UCB of class #1 is equal to the LCB of class #2. The UCB of class #2 is equal to the LCB of class #3. In general, the UCB of a class is equal to the LCB of the next class.
Class width
No less important is the concept of class width or class size. Class width, c, of a class is equal to the difference between the class boundaries, that is, c = UCB – LCB. In Table 4, the class #1’s width is c = 9.95 – 4.95 = 5.0. Similarly, the class width of class #2 is c = 14.95 – 9.95 = 5.0. Note that in Table 4, all classes have the same class width. The classes of a frequency distribution table don’t necessarily have an equal class width. It is allowable to construct a frequency distribution table with unequal class widths, as instanced in the following table.
As you may verify, the first three classes have the width of $10, the fourth class is $20 width, and the fifth class has the width of $30.
