1.4 Representing a Categorical Variable with Graphs

Bar Graphs

To construct a bar graph (bar chart), we mark the frequencies on a vertical axis and the categories on the horizontal axis. Each category represents one bar. The frequency of each category determines the heights of the bars. All bars have the same width and gap between adjacent bars. To keep it short, here is the bar graph of stress on the job. We can also use relative frequencies or percentages to construct the bar graph. You can be creative and color each category with a different color. It will be  visually attractive and easier to compare them.

Source: Prem S. Mann: Introductory Statistics. John Wiley and Sons Inc. 2020

Pie Charts

A pie chart is more commonly used to display percentages though not limited to frequencies or relative frequencies. The whole pie is divided into different portions that represent the different categories. Now we can use the same example and the percentages from the relative frequency table to display the pie the responses on job stress.

Tips: The choice between bar graphs and pie charts will depend on how many categories that variable of your interest assumes and the size of it. Whenever you have many categories or few categories with about the same frequencies, then the bar graph should be your first choice. If the pie has many slices or slices of the same size, it will be hard to compare the groups. Next, be careful of quantity distortions and keeping the area principle.

Contingency Table (Two-Way Table)

Categorical data can also be organized in contingency tables. The table shows how the individuals are distributed in the cells contingent with other variables. Contingency tables can tell how the variables are related to each other. When the numbers in cells are the same for all categories, then we can say that the variables are independent of each other. This is all about contingency tables; you will explore more about it in the coming units.🎥Watch: AP Stats - Analyzing Categorical Data

Resources:

Key Vocabulary

• Frequency Table

• Relative Frequency Table

• Pie Chart

• Bar Graph

• Two-way Table