Summary of Displaying Categorical Data

In this section, you first looked at the Young People Survey[1] to describe characteristics in the data set about the drinking habits, music appreciation, and punctuality of surveyed young adults. Then you examined characteristics in the data from a Sleep Study[2]. Reflect for a moment upon how you answered the questions posed in the previous two activities. Then, for each of the objectives listed below, use the slider to indicate your level of comfort being able to perform them on a formal assessment.

Monitoring Your Readiness

To effectively plan and use your time wisely, it helps to think about what you know and do not know. For each of the following, rate how confident you are that you can successfully do that skill. Use the following descriptions to rate yourself:

5—I am extremely confident I can do this task.

4—I am somewhat confident I can do this task.

3—I am not sure how confident I am.

2—I am not very confident I can do this task.

1—I am definitely not confident I can do this task.

Skills Needed for Displaying Categorical Data: Forming Connections

Skill or Concept: I can . . . Questions to check your understanding Rating from 1 to 5
Determine which variables are categorical from raw data. 1
Understand how frequency tables are formed from raw data. 2
Use data analysis tools to create a frequency table from an embedded data set. 3, 4
Understand how graphs for categorical data are formed from frequency tables. 5
Read frequency tables, bar graphs, and pie charts. 7, 8

Now use the ratings to get ready for your next in-class activity. If your rating is a 3 or below, you should get help with the material before class. Remember, your instructor is going to assume that you are confident with the material and will not take class time to answer questions about it.

Ways to get help:

  • See your instructor before class for help.
  • Ask your instructor for on-campus resources.
  • Set up a study group with classmates so you can help each other.
  • Work with a tutor.

Essential Concepts

  • Categorical variables have distinguishing features placing individuals into one of several groups such as eye color, zip code, education level, and gender. The data from these variables can be displayed in multiple ways.
  • Frequency tables, bar graphs, and pie charts are created to display the distribution of categorical variables.
  • Completing frequency tables can be done by hand, but technology is needed to display frequency tables for larger data sets.
  • 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.
  • The data distributions that result in using technology to create graphical displays (frequency tables, bar graphs, and pie charts) are used to answer questions about categorical variables.

Study Tips: Evidence-based strategies for learning

  • Test your understanding of categorical variables by creating flashcards from the examples given in the text and assignments. Pay particular attention to variables that contain numbers but that are categorical in nature such as zip-code or salary ranges.
  • Practice completing the frequency tables given in the text and assignments by writing them out on a blank page by hand. Take pauses as you write them out to explain what you are doing out loud.
  • Explain to a friend, real or imaginary, which kinds of graphs and charts can be used to display distributions of categorical variables. Point out which display is better to use for different situations, different types of distributions, or to answer different questions.
    • Perform this in turns in your study group or, if studying alone, use the video feature on your phone to see your own explanation.
    • In your study group, critique one another’s explanation (or refer to the information from the text and assignments to check your accuracy if studying alone).
  • Put the glossary terms into a collection of flashcards. Study them in short bursts a few times each week throughout the course in preparation for high stakes tests such as a midterm or the final exam.

Foundational Knowledge

Key Equations

  • Converting a fraction to a proportion

  [latex]\dfrac{\text{frequency (count)}}{\text{total frequency}}[/latex]

  • Converting a proportion to a percentage

   [latex]\text{proportion (decimal form)} \times100[/latex], then append a percent symbol, %.

  • Converting a percentage into a number given a total

  [latex]\text{percentage (decimal form)} \times\text{total number given}[/latex]

Glossary

bar graph
a graph in which the categories are represented by bars that are separated from each other.
categorical variable
a variable that places an individual into one of several groups.
data set
a collection of data.
frequency
the number of times an event or a value occurs. It is commonly referred to as the count.
frequency table
a table that lists the number of observations (the frequency or count) of each unique value of a categorical variable.
pie chart
a chart in which categories are represented by wedges in a circle and are proportional in size to the percentage of individuals/items in each category.
quantitative variable
a variable that takes numerical values that can be used in arithmetic.
relative frequency
the proportion of observations that are in a particular category and can be expressed as a decimal or a percentage.

 

My Skills Checklist:

  • I can display categorical data in multiple ways.
  • I can create frequency tables to display the distribution of categorial variables.
  • I can create bar graphs to display the distribution of categorial variables.
  • I can create pie charts to display the distribution of categorial variables.
  • I can use data distributions displayed in tables and graphs to answer research questions.

 

Check mark list on clipboard

Topic Complete – now test your understanding in the Self-Check.

  1. Young people survey. (2016, December 6). Kaggle. Retrieved from https://www.kaggle.com/miroslavsabo/young-people-survey ↵
  2. Onyper, S., Thacher, P., Gilbert, J., & Gradess, S. (2012). Class start times, sleep, and academic performance in college: A path analysis. Chronobiology International, 29(3): 318–335. ↵