Frequency Table

Frequency Tables for Distributions with Ungrouped Scores

Frequency distributions with ungrouped scores are presented in tables showing the scores in the first column and how often each score has occurred (the frequency) in the second. They are typically used for discrete variables, which have a countable or finite number of distinct values. Tables of ungrouped scores are also used when the number of different scores a variable can take in a data set is low.

Two steps must be followed to build up a frequency table out of a set of data: (a) Construct a sensible array using the given set of data, and (b) count the number of times each score occurs in the given data set. The raw data in Table 1 show the number of children families have in a small community.

Building up an array implies arranging the scores in an ascending or descending order. An ascending array is built for the data set in Table 2.

The number of times each score occurs in the data set is then counted, and the total is displayed for each score, as in Table 3.

Frequencies measure the number of times each score occurs. This means that one family has no children, and four families have five children each. Although some scores may not occur in the sample data, these scores must nevertheless be listed in the table. For example, even if there are no families with only one child, the score of 1 is still displayed together with its corresponding frequency (zero) in the ascending array built out of the sample data.

Relative frequencies, also called proportions, are computed as frequencies divided by the sample size: rf = f/n. In this equation, rf represents the relative frequency corresponding to a particular score, f represents the frequency corresponding to the same score, and n represents the total number of cases in the analyzed sample. They indicate the proportion of observations corresponding to each score. For example, the proportion of families with two children in the analyzed community is 0.20.

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