A grouped frequency table can be used to illustrate a hypothetical distribution of simple reaction times for a sample of $$20$$ participants. Since reaction times encompass a wide range of continuous values, the first column lists ranges of equal width—specifically, intervals such as $$141$$ to $$160$$, $$161$$ to $$180$$, and up to $$241$$ to $$260$$ milliseconds. The second column displays the frequency of participants whose reaction times fall into each respective interval. For instance, the table shows that $$9$$ participants had reaction times in the $$181$$ to $$200$$ millisecond range, effectively summarizing the data into manageable groups.

Grouped Frequency Table of Reaction Times

When constructing a grouped frequency table to summarize a dataset with a broad range of scores, what information is typically displayed in the first column?

When a dataset contains a large number of different scores spanning a broad range, it is often more effective to summarize the data using a grouped frequency table. Instead of listing individual scores, the first column displays ranges of values (typically between $$5$$ and $$15$$ equal-width intervals), and the second column shows the frequency of scores falling into each of those ranges.

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A frequency table is a tabular method used to display the distribution of a variable. It organizes data by listing the possible values of the variable in one column and the frequency—the number of times each score occurs—in a second column. For numerical data, the values are typically ordered from highest at the top to lowest at the bottom, and only the range of scores actually present in the dataset is included. This format allows researchers to quickly observe important features of the distribution, such as the range of scores, the most and least common values, and any extreme outliers.

Frequency Table

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Grouped Frequency Table

Frequency tables can also be used to display the distribution of categorical variables. In this application, the first column lists the category labels rather than numerical values. While the ordering of these categories is somewhat arbitrary, they are frequently arranged from the most common category at the top to the least common at the bottom.

Frequency Tables for Categorical Variables

A practical illustration of a frequency table involves a hypothetical distribution of scores on the Rosenberg Self-Esteem Scale for a sample of $$40$$ college students. In this table, the first column lists the individual self-esteem scores descending from $$24$$ down to $$15$$. The second column indicates the frequency of each score, revealing that $$3$$ students scored $$24$$, $$5$$ students scored $$23$$, and $$10$$ students scored $$22$$. By organizing the data this way, it becomes immediately apparent that the scores range from $$15$$ to $$24$$, the most common score is $$22$$, and the least common score is $$17$$, which has a frequency of $$0$$.

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