Choosing chart types – misleading graphs

MathematicsStatisticsAges 13–14

Use with my class

The same dataset is drawn as a bar chart, grouped bar chart, line graph, and pie chart. Students switch chart types, drag the top of a bar to change the values, and drag a slider so the y-axis does not start at 0 to see how much the difference gets exaggerated. The simulation comments on which chart type fits the data and flags misleading graphs.

Lesson: Choosing an appropriate chart type. Interpreting statistical data from graphs

What it shows

Choosing a chart starts with the kind of data. Parts of a whole, such as the ways students travel to school, suit a pie chart; values measured over time suit a line graph; comparisons between categories suit bars, and a grouped bar chart puts two series, such as two years or two cities, side by side. The simulation also exposes a common trick: when the y-axis does not start at 0, bar heights stop being proportional to the values, so a small real difference looks several times larger. It calculates both the apparent and the real ratio of the tallest bar to the shortest.

How to use

Pick a Dataset and switch between Bar, Grouped bar, Line and Pie, reading the comment that says whether the chart type fits. Then return to Bar and move the Y-axis starts at slider upwards, comparing the apparent ratio with the real one in the warning. Drag bar tops to change values and see how the exaggeration changes, and use Reset data to restore the original table. Graphs from newspapers or advertisements make a good follow-up.

Parameters you can change

  • Dataset Revenue by quarter, Sport chosen by students (number of students), Average monthly temperature (°C), Way to school (%)
  • Chart type Bar, Grouped bar, Line, Pie
  • Y-axis starts at (% of minimum value) 0–90 %
  • Show comment/warning
  • Show values on chart
  • Currency From the language, US dollar, Euro, Indian rupee, Indonesian rupiah, Saudi riyal

Questions to explore

  1. Why does starting the y-axis above 0 make a small difference look much larger?
  2. Which chart type suits the way-to-school data, and why?
  3. When is a grouped bar chart more useful than a simple bar chart?