Descriptive Statistics > Area Principle

## What is the Area Principle?

The area principle states that the area of a graph should equal the magnitude of the data it is representing. For a simple example, let’s say you took three height measurements of 4 feet, 5 feet, and 6 feet. **The top part of the image below shows data that agrees with the area principle**:

- The 4 feet measurement has an area of 4 (1 unit up * 4 units across);
- The 5 feet measurement has an area of 5 (1 unit up * 5 units across);
- The 6 feet measurement has an area of 6 (1 unit up * 5 units across);

**The bottom part shows data that violates the area principle.** The eye is drawn towards the 4 foot measurement because of the increased area that is out of proportion to the measurement. Even though 6 feet is clearly the larger measurement, the eye is drawn to the larger area.

- The 4 feet measurement has an area of 8 (2 units up * 4 units across);
- The 5 feet measurement has an area of 5 (1 unit up * 5 units across);
- The 6 feet measurement has an area of 6 (1 unit up * 5 units across);

## The Area Principle and 3D Pie Charts

This 3D graph makes it look like the yellow wedge is about the same size (or even larger) as the green wedge. If you look at the key, and at the surface area of the wedges, you’ll notice the green wedge is actually 10% larger. Not all 3D software obeys the principle rule, so check your graph after you make it.

## The Area Principle and Bar Charts

Bar charts can violate the area principle if the vertical axis starts at a number other than zero. This tactic is one commonly employed by the media to make numbers look scarier than they actually are. This graph comes from Fox News, which clearly showed the disaster that would happen if Bush’s tax cuts expired. Notice the vertical axis starting on the right at 34.

Vertical axes usually start on the left, at zero. The placement of the axis on the right is probably deliberate, as the casual viewer would be looking on the left for the axis, and not seeing it, would only see the “huge” jump in tax rates. The tax rate jump would be, in fact, only about 4.6%.

## References

Tabor, J. & Franklin, C. (2011). Statistical Reasoning in Sports. W. H. Freeman.

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**Stephanie Glen**. "Area Principle in Statistics" From

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