# 2.1.1.2 - Visual Representations

Frequency tables, pie charts, and bar charts can all be used to display data concerning one categorical (i.e., nominal- or ordinal-level) variable. Below are descriptions for each along with some examples. At the end of this lesson you will learn how to construct each of these using Minitab Express.

frequency table contains the counts of how often each value occurs in the dataset. Some statistical software, such as Minitab Express, will use the term tally to describe a frequency table. Frequency tables are most commonly used with nominal- and ordinal-level variables, though they may also be used with interval- or ratio-level variables if there are a limited number of possible outcomes.

In addition to containing counts, some frequency tables may also include the percent of the dataset that falls into each category, and some may include cumulative values. A cumulative count is the number of cases in that category and all previous categories. A cumulative percent is the percent in that category and all previous categories. Cumulative counts and cumulative percentages should only be presented when the data are at least ordinal-level.

The first example is a frequency table displaying the counts and percentages for Penn State undergraduate student enrollment by campus. Because this is a nominal-level variable, cumulative values were not included.

Frequencies of Campus
Campus Count Percent
University Park 40,639 50.1%
Commonwealth Campuses 27,100 33.4%
PA College of Technology 4,981 6.1%
World Campus 8,360 10.3%
Total 81,080 100%

Penn State Fall 2019 Undergraduate Enrollments

The next example is a frequency table for an ordinal-level variable: class standing. Because ordinal-level variables have a meaningful order, we sometimes want to look at the cumulative counts or cumulative percents, which tell us the number or percent of cases at or below that level.

As an example, let's interpret the values in the "Sophomore" row. There are 22 sophomore students in this sample. There are 27 students who are sophomore or below (i.e., first-year or sophomore). In terms of percentages, 34.4% of students are sophomores and 42.2% of students are sophomores or below.

Frequencies of Class Standing
Class Standing Count Cumulative Count Percent Cumulative Percent
First-Year 5 5 7.8% 7.8%
Sophomore 22 27 34.4% 42.2%
Junior 17 44 26.6% 68.8%
Senior 20 64 31.3% 100.0%

A pie chart displays data concerning one categorical variable by partitioning a circle into "slices" that represent the proportion in each category. When constructing a pie chart, pay special attention to the colors being used to ensure that it is accessible to individuals with different types of colorblindness.

A bar chart is a graph that can be used to display data concerning one nominal- or ordinal-level variable. The bars, which may be vertical or horizontal, symbolize the number of cases in each category. Note that the bars on a bar chart are separated by spaces; this communicates that this a categorical variable.

The first example below is a bar chart with vertical bars. The second example is a bar chart with horizontal bars. Both examples are displaying the same data. On both charts, the size of the bar represents the number of cases in that category.

Pie charts tend to work best when there are only a few categories. If a variable has many categories, a pie chart may be difficult to read. In those cases, a frequency table or bar chart may be more appropriate. Each visual display has its own strengths and weaknesses. When first starting out, you may need to make a few different types of displays to determine which most clearly communicates your data.