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Frequency distribution tables, as I am sure you will agree, are great tools to organize data. But, of course, a picture is worth 1,000 words. So in addition to frequency distribution tables, frequency distribution graphs can be helpful in understanding a dataset. In fact, in psychological research, it is more common to see a frequency distribution graph than a similar type of table. Let’s now discuss the three major types of frequency distribution graphs.

A critical consideration in selecting a frequency distribution graph is the scale of measurement for a variable. In the previous chapter, we discussed nominal, ordinal, and scale measurements. If our data are nominal, we use what’s called a bar graph. If our data are ordinal or scale, we use what are called histograms and frequency polygons.

A bar graph uses vertical bars above each category listed on the x-axis to display the frequency for a category. There is a space between the bars because each category is distinctly different from the other categories. For example, Figure 3.1 contains a bar graph for a nominal variable in Wendt’s (2013) research, students’ year in college. This is a nominal variable because each participant was either a first-year or a senior. No person could be in both categories.

Bar graph: graphical representation of the frequency of nominal data in which each category appears on the x-axis and the frequency of occurrence for a given score appears on the y-axis.

Looking closely at Figure 3.1, notice that each category is listed on the x-axis, with the name of the variable beneath the category names. Each bar is centered above its category name. There is a space between the two bars because there can be no overlap between the categories; that is, a first-year cannot be a senior, and a senior cannot be a first-year. Finally, the y-axis provides the frequency numbers.

Figure 3.1 Displaying Frequency Nominal Data With a Bar Graph

Whereas a bar graph is used for nominal data, we use a histogram for ordinal and scale data. Once again we have the values of a variable on the x-axis and the frequencies on the y-axis. A histogram for Wendt’s (2013) burnout scores appears in Figure 3.2. Notice here how there is no space between the values along the x-axis as there was for a bar graph. Because we are dealing with scale data, we have values that inherently increase as we move from the left to the right side of the axis (the same would be true of ordinal data). If you look back at the bar graph in Figure 3.1, there is no reason that the category of “senior” could not appear before the category of “first-year.”¹

Figure 3.2 Displaying Frequency Scale Data With a Histogram

Histogram: similar to a bar graph, except used for ordinal and scale data that are discrete; that is, each score is different from all other scores.

Similar to histograms, frequency polygons are used for ordinal and scale data. Rather than bars, a polygon uses a line graph to display the frequency of scores or categories of scores. We again have scores or categories of scores on the x-axis and frequencies on the y-axis. With each frequency plotted, we place a dot centered above each category score. We then connect the dots to form a polygon, such as the one in Figure 3.3. Frequency polygons are particularly helpful in displaying frequencies for continuous data, which, as you’ll recall from the previous chapter, can take on any fractional value along the x-axis (such as time, which can be measured in seconds or fractions of seconds). Histograms are better to use with discrete data, such as the burnout scores, which could take on only a whole-number value in Wendt’s (2013) research.

Figure 3.3 Displaying Frequency Scale Data With a Frequency Polygon

Frequency polygon: line graph that displays frequency of occurrence of scores; used for continuous data.