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Grade 12

Cropped Graphs (Investigation)

Lesson

Cropped graphs

Graphs can also be misleading if large sections are cropped off. The bar graph to the right is an instance of this deceptive practice. It shows the results of a poll in the US that asked people whether they agreed or disagreed with a particular court’s decision. Here, the bottom sections of the bars and the bottom section of the vertical axis have been cut off. This has created the impression that there is a lot of support for the court’s decision among Democrats, but very little support among Republicans and Independents. Yet the difference between the levels of support between Democrats and Republicans/Independents is only 62% - 54% = 8%.

The bar graph to the right shows how the original graph would have appeared if the bottom sections of the bars had not been cut off. Here you can see that the difference in the support for the court’s decision between Democrats, Republicans and Independents is actually quite small. As you can see, it is quite easy to be fooled when large sections of a graph are cut off. But don’t despair. You can easily know when someone is using this trick by checking if the scale starts at some number other than 0. For instance, the above graph started at 53, not 0.

Discussion

The above bar graph shows the top tax rate that would prevail under the tax plan of some presidential candidate.

  1. Has the author used cropping in this instance? If so, how?
  2. Explain how this could be misleading.
  3. Redraw the graph so that it is not misleading.

Outcomes

12C.D.2.3

Interpret statistics presented in the media, and explain how the media, the advertising industry, and others (e.g., marketers, pollsters) use and misuse statistics (e.g., as represented in graphs) to promote a certain point of view

12C.D.2.4

Assess the validity of conclusions presented in the media by examining sources of data, including Internet sources (i.e., to determine whether they are authoritative, reliable, unbiased, and current), methods of data collection, and possible sources of bias (e.g., sampling bias, non-response bias, a bias in a survey question), and by questioning the analysis of the data (e.g., whether there is any indication of the sample size in the analysis) and conclusions drawn from the data (e.g., whether any assumptions are made about cause and effect)

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