Linda L. Cooper & Felice S. Shore (2010) The Effects of Data and Graph Type on Concepts and Visualizations of Variability, Journal of Statistics Education, 18:2, DOI: 10.1080/10691898.2010.11889487

Summarize research question:

How to visualize variability using:

  • Histogram
  • Distribution bar graphs
  • Bar value charts

Approach and methods

It’s just like, our opinion, man.


  • Bar Value Chart: Horizontal line for the mean. Then how far the tops of the bars are away from the horizontal line tells us how much variability (figure 1)
  • Histogram: vertical line for mean. Then how far away and how many from the vertical gives the variability. (figure 5)
  • Distribution bar graphs: find mode. If most of the stuff is in there, then there’s low variability. Opposite of how you determine variability in a bar value chart.


You should do what we say so the public has better media numeracy.

Possible application(s) to curriculum:

  • Activity where we have kids draw one chart from a different chart.
  • Focused learning segment just on reading and interpreting graph axes.
  • Juxtapose value bar graph and histogram, explicitly showing how to determine spread.

Other notes

I made the same error described about the U-shaped distribution. I was confused when they said that distribution had low variability because it certainly looked like most of the data was clustered around two thingies. That doesn’t seem very spread out. But later, when they described “more variable” as “deviate more from the mean”, THAT made sense. I think it’s important that we make this subtlety clear to students as soon as we are able.