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Slope in the Coordinate Plane

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How to Lie with Graphs

Credit: Laura Guerin
Source: CK-12 Foundation
License: CC BY-NC 3.0

Imagine two graphs. The first graph looks very steep. The second graph looks nearly flat. It's obvious that whatever the first graph measures is changing very fast, while the measurements in the second graph are changing really slowly, right? Don′t jump to conclusions. Unless you figure out the actual slope of both graphs, you can't really know their rates of change.

News You Can Use

Newspapers, bloggers, politicians, and activists all can manipulate their graphs to make dramatic points. The same information can produce a steep line or a nearly flat line—it all depends on how you set the scale. For example, the two graphs below each show the same line (y=x+1). Even though both graphs have the same slope, it looks like the graph on the left has a steeper slope than the graph on the right because of how the y-axes are scaled.

Credit: Laura Guerin
Source: CK-12 Foundation
License: CC BY-NC 3.0

What should you do when you see a particularly dramatic graph? Look at the scales and calculate the slope for yourself. Don’t fall for visual scaling tricks. Use your math skills to test the data and see what it really says.

A community college professor in California has collected misleading graphs. He pairs them with corrected graphs so that his students can compare them.

See for yourself: http://wserver.scc.losrios.edu/~harbism/discussion.pdf

Explore More

Here are more examples of how misleading graphs can cause people to misinterpret data. Keep them in mind the next time you’re looking at a graph that claims to show big changes.

http://voices.washingtonpost.com/ezra-klein/2010/09/lies_damn_lies_and_the_y_axis.html

http://passyworldofmathematics.com/misleading-graphs/

http://www.forbes.com/sites/naomirobbins/2012/08/28/must-zero-be-included-on-scales-of-graphs-another-look-at-fox-news-graph-and-huffs-gee-whiz-graph/#

http://www.fallacyfiles.org/archive062012.html#06042012

Image Attributions

  1. [1]^ Credit: Laura Guerin; Source: CK-12 Foundation; License: CC BY-NC 3.0
  2. [2]^ Credit: Laura Guerin; Source: CK-12 Foundation; License: CC BY-NC 3.0

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