Frequency Distributions

Constructing a Frequency Distribution Table

Frequency distribution tables describe a sample population. Generally speaking, a frequency distribution table presents the categories, number of occurrences, relative frequency, and percentage of total. Categories in a frequency distribution table must be comprehensive and mutually exclusive. Comprehensive means that the categories include the entire range of data. Mutually exclusive means that each occurrence fits in only one category, preventing double counting and/or data omission. The exemplar data set in Table 1 illustrates a sample population of 50 individuals and their annual income.

Table 1 Example Data Set

[Page 595]The first step in building the table involves evaluating minimum, maximum, and range. The minimum and maximum represent the smallest and largest value in the data set, respectively. The range expresses the difference between the minimum and maximum. In the Table 1 example set, the minimum is $0, maximum is $99,900, and the range is $0 to $99,900. Although determining number of categories to employ is subjective, the goal is to maximize descriptive value while gradually and thoughtfully increasing number of groupings with larger data sets. Ideally, intervals of data end on a data point used in that interval.

Based on the sample size and range of data, this example uses a selection of five interval categories: $0–20,000, $20,001–40,000, $40,001–60,000, $60,001–80,000, and $80,001–100,000. These groups are comprehensive and mutually exclusive; encompassing the entire range and allowing each salary to fit in one, and only one, category. Table 2 presents four columns. The first column describes each interval; in this example, the salary range. The second column lists the number of occurrences in the sample that correspond with the category. The third column calculates relative frequency, the frequency divided by the total, whereas the fourth column cites relative frequency as a percentage of the population.

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