Frequency Distribution

It is not only important to understand what descriptive data represent but, if possible, to see it as well. One way to do this is through the use of a frequency distribution, a visual representation of a distribution of data.

Table 1 shows 25 scores on a math test for which a frequency distribution will be created.

The first step in creating a frequency distribution is to define the class interval that will be used. A class interval is a range of numbers, and the first step in the creation of a frequency distribution is to define how large each interval will be.

Some guidelines for creating a class interval are as follows:

• 1.
  Select a class interval that has a range of 2, 5, 10, 15, or 20 data points.
• 2.
  Select a class interval so that 5 to 20 such intervals cover the entire range of data. A convenient way to do this is to compute the range, then divide by a number that represents the number of intervals you want to use (between 10 and 20).
• 3.
  Begin listing the class interval with a multiple of that interval.
• 4.
  Finally, the largest interval goes at the top of the frequency distribution.

Once class intervals are created, it is time to complete the frequency part of the frequency distribution. This is done simply by counting the number of times a score occurs in the raw data and entering that number in each of the class intervals represented by the count.

In the frequency distribution created earlier, the number of scores that occur between 80 and 84 and are in the 80–84 class interval is 8. So, an 8 goes in the column marked Frequency.

Table 2 shows the frequency distribution following the guidelines listed previously where all 25 scores are represented and can, of course, only appear in one interval.

Another way to visualize a distribution of scores is through the creation of a histogram such as that depicted in Figure 1.

Figure 1 Sample Math Scores—Histogram