Wiki Page, Math 13 - Perez Sandbox : Module 10 - Two-Way Tables (1 of 5)

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The Distribution of a Categorical Variable

We begin our discussion by analyzing the distribution of a single categorical variable. We cannot see patterns easily by looking at a spreadsheet of data, so we summarize the distribution in a table.

Previously, when we summarized the distribution of a quantitative variable, we made a graph (dotplot, histogram, or boxplot) that showed

the possible values of the variable

the number of individuals with each variable value or interval of values.

Here we use a table to summarize the distribution of a categorical variable. We create a table so we can see

the different values (categories) the variable takes.

how many times each value occurs (count) and, more important, how often each value occurs (by converting the counts to proportions or percentages).

EXAMPLE Describing the distribution of a categorical variable

What is your perception of your own body? Do you feel that you are overweight, underweight, or about right? A random sample of 1,200 U.S. college students answered this last question as part of a larger survey.

Here is the table categorizing the results:

Summary of body perception

Category | Count | Proportion | Percentage
underweight | 110 | 110/1,200 = 0.092 | 9.2%
overweight | 235 | 235/1,200 = 0.196 | 19.6%
about right | 855 | 855/1,200 = 0.713 | 71.3%
TOTAL | 1,200 | XXXXXXXXX | 100.1%

This distribution is completely described by the three percentages 9.2%, 19.6%, and 71.3%, which correspond to the three categories of the body image variable: “underweight,” “overweight,” and “about right.”

(Note that the percentages add up to 100.1% instead of 100% because we rounded percentages to three decimal places.)

We can use a stacked bar chart to display the distribution of the body image variable.

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