1. 1: Analyzing Categorical Data



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bar graph or pie chart.







    • Bar graphs represent each category as a bar.

      • The bar heights show the category counts or percents.

      • Bar graphs are

        • Easier to make than pie charts

        • Easier to read

        • More flexible than pie charts

      • Tip: When you draw a bar graph, make the bars equally wide.



Ex: Frequent superpower? An on-line survey asked which superpower high-school students would choose to have—fly, freeze time, invisibility, super strength, or telepathy. Here are the responses from the 40 randomly selected students in the sample:

Fly Freeze time Telepathy Fly Telepathy Super strength Telepathy Telepathy Fly

Super strength Invisibility Freeze time Fly Telepathy Freeze time Telepathy Super strength Fly Freeze time Telepathy Freeze time Freeze time Freeze time Fly Fly Fly Freeze time

Invisibility Fly Invisibility Telepathy Telepathy Fly Telepathy Fly Fly Telepathy Telepathy Fly Fly
Make an appropriate graph to display the distribution of superpower preference. Describe what you see.


Ex: Social media The Pew Research Center surveyed a random sample of U.S. teens and adults about their use of social media in 2013. The pictograph on the right displays some results.

  1. Explain how this graph is misleading.




  1. Make a bar graph that displays the results in a non-misleading way.



  1. Would it be appropriate to display these results in a pie chart? Why or why not?


Ex: Two possible bar graphs of the data are shown below. Which one could be considered deceptive? Why?


  • Relationships Between Two or More Categorical Variables

    • When a dataset involves two or more categorical variables, we begin by examining the counts or percents in various categories for one of the variables.

    • A two-way table describes two categorical variables, organizing counts according to a row variable and a column variable.

      • Ex: A survey of 4826 randomly selected young adults (aged 19 to 25) asked, “What do you think the chances are you will have much more than a middle-class income at age 30?” The table on the right shows the responses.


    • The marginal distribution of one of the categorical variables in a two-way table of counts is the distribution of values of that variable among all individuals described by the table.

    • Note: Percents are often more informative than counts, especially when comparing groups of different sizes.


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