When describing data using graphical representations, certain variables in the data are appropriate for certain visualizations. To prepare for the upcoming activity, you will need to identify variables that would be appropriate for bar graphs and pie charts and answer research questions by reading bar graphs and pie charts. To do this, you will need to be able to determine which variables in a dataset are categorical, understand how frequency tables are formed, and understand how bar graphs and pie charts are formed.

Categorical Variables

In Module 1, Data Collection and Organization, you learned the difference between categorical and quantitative variables. Let’s take a moment to refresh that information before diving into a deep exploration of categorical variables.

Practice identifying categorical variables in a list in the example. Then, for the data table that follows, identify the categorical variables to answer Question 1.

Now it’s your turn to practice what you know by looking at a real dataset obtained from a survey and displayed in the table below. Read the information given about the dataset and its variables, then answer the questions that follow.

Variables in a dataset

In 2013, students of the statistics class at FSEV UK, a Slovakian University, were asked to invite their friends to participate in a survey^[1]. Data for the first [latex]15[/latex] out of [latex]1,007[/latex] young people who completed the survey are displayed below.

The following eight variables are included in the dataset. The variable names are presented in italics, followed by a brief description. You may recall from Forming Connections in (1D) that this is often called a data dictionary.

• Alcohol: “never,” “social drinker,” or “drink a lot”
• Age: Years
• Height: Height in centimeters (cm)
• Punctuality: “I am often early,” “I am often on time,” or “I am often running late”
• Number of siblings
• Enjoy music: Participants were asked “Do you enjoy music?” and reported on a 5-point Likert scale: strongly disagree = 1, strongly agree = 5
• Internet usage: “no time at all,” “less than an hour a day,” “few hours a day,” or “most of the day”
• Left – right handed

Frequency Tables

A frequency table lists the number of observations (the frequency) of each unique value of a categorical variable. The frequency is commonly referred to as the count. See the example below, which illustrates a partially complete, simple frequency table for a survey in which [latex]20[/latex] people were asked to answer a question by choosing one of four responses: strongly disagree, disagree, agree, or strongly agree.

Interpreting frequency tables

Frequency tables often include a column for the relative frequency. The relative frequency represents the proportion of observations that are in a particular category and can be expressed as a decimal or a percentage. To find relative frequency, divide the count of a particular category by the sum of all the counts. See the recall box below for a refresher on how to convert ratios to proportions and percentages. Also see the Student Resources: Fractions, Decimals, Percentages and Ratios and Fractions.

The following frequency table displays the frequency and relative frequency (as a decimal and a percentage) of the categorical variable Alcohol for the first [latex]15[/latex] young people who responded to the survey.

Building tables from data

Displaying frequency tables for small datasets might be feasible by hand, but we need technology to display frequency tables for larger datasets.

Let’s use technology to create a frequency table to understand the variable Enjoy Music for all [latex]1,007[/latex] students included in the survey. Follow these steps:

Refer to the frequency table you just created to answer Questions 3 and 4.

When exploring categorical data, it is helpful to convert the data from tables into charts or graphs. Bar graphs and pie charts provide visual summaries of data that help us quickly identify how the individual category frequencies relate to one another and to the total count.

Bar Graphs

One of the most commonly used graphs for visualizing the distribution of a categorical variable is a bar graph. In a bar graph, categories are represented by bars that are separated from each other. The bars can be vertical or horizontal, and the height (or length) of each bar represents the measure of the data in each category. Bars can represent frequencies, relative frequencies (proportion), or percentages.

Interpreting bar graphs

At this point, students will be presented with two datasets. They will be able to choose which one they would like to use to answer example questions before creating bar graphs using the data analysis tool.

The bar graph below displays the number of cones each of a small ice cream shop sold on the 4th of July. Note that the counts (numbers of cones) are listed on the vertical axis while each flavor sold is listed along the horizontal axis. Examine the graph, then answer the questions in the Example that follows.

Now that you have had a chance to become familiar with this categorical visualization, follow the directions below to use technology to create a bar graph for a real dataset.

Creating bar graphs from data

Recall the frequency table you created earlier in this section using the Describing and Exploring Categorical Data tool. When you used the technology tool to create the frequency table, a bar graph was also created on that page. Let’s go back to the tool to explore the bar graph. If you still have the tool open for this dataset, just follow steps 4 and 5 below to view the bar graph.

Take a moment to explore switching these options back and forth to see how the graph changes then answer Question 5 below.

Pie Charts

Another common graph used for displaying the distribution of categorical data is a pie chart. In a pie chart, categories are represented by wedges in a circle and are proportional in size to the percentage of individuals/items in each category. There are several ways to present pie chart data visually. A pie chart may include all the information needed to read it within each wedge or they may provided some image in the chart and some in a key off to the side.

Interpreting pie charts

Pie charts are useful for showing percentages (parts of a whole) at some particular instance in time. For example, the following chart displays flavors of ice cream sold at an ice cream shop as a percentage of all ice cream sales on July 4th. This chart contains the same information as the bar chart does above, but shows percentages rather than counts.

Creating pie charts from data

When you used the Describing and Exploring Categorical Data data tool to create the frequency table and bar graph, you also had the option to create a pie chart. Let’s do that now. If you still have the tool open, skip to Step 4 below.

It’s difficult to visualize a summary of the Enjoy music categories since just one or two of them dominate the chart. Let’s leave the tool now and explore another one of the variables from the dataset: Punctuality. The following pie chart displays the distribution of the categorical variable Punctuality. Use this pie chart to answer Questions 7 and 8 below.

Summary

In this preview section, you’ve had a chance to practice the tasks that will be essential to forming deeper connections in the next activity. This is a good time to sum it all up before moving on.

• In question 1, you identified categorical variables from a list of variables appearing in raw data.
• In question 2, you completed a frequency table from raw data by hand.
• In question 3, you used technology to create a frequency table from raw data.
• In question 4, you used technology to create and manipulate a graph of categorical data from a frequency table.
• And in questions 3 – 5, you read a frequency table, a bar graph, and a pie chart to make observations about categorical data.

You’ve seen in this section that frequency tables, bar graphs, and pie charts are all good tools for visualizing categorical data. If you feel comfortable with these ideas, it’s time to move on!