Drawing a Two-Way Frequency Table

Organizing data in a two-way frequency table can help with visualization, which in turn makes it easier to analyze and present the data. To draw a two-way frequency table, three steps must be followed.

1. Determine the categories.
2. Fill the table with the given data.
3. Determine if there are any missing frequencies. If so, find those.

Suppose that 53 people took part in an online survey, where they were asked whether they prefer top hats or berets. Out of the 18 males that participated, 12 prefer berets. Also, 15 of the females chose top hats as their preference. The steps listed above will now be used to analyze and present the data.

1

Determine the Categories

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First, the two categories of the table must be determined, after which the table can be drawn without frequencies. Here, the participants gave their hat preference and their gender, which are the two categories. Hat preference can be further divided into top hat and beret, and gender into female and male.

The total row and total column are included to write the marginal frequencies.

2

Fill the Table With Given Data

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The given joint and marginal frequencies can now be added to the table.

3

Find Any Missing Frequencies

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Using the given frequencies, more information can potentially be found by reasoning. For instance, because 12 out of the 18 males prefer berets, the number of males who prefer top hats is equal to the difference between these two values. 18 - 12 = 6 Therefore, there are 6 males who prefer top hats. Since there are 15 females who prefer top hats, the number of participants who prefer this type of hat is the sum of these two values. 6 + 15 = 21 It has been found that 21 participants prefer top hats. Continuing with this reasoning, the entire table can be completed.