2. That area scales with the square of length, and volume with the cube of length, has important consequences for the depiction and interpretation of data graphics. Suppose we wish to indicate in an artistic way that the disposable income (after taxes) of a typical U.S. worker is twice that of a typical worker in France, by showing that the U.S. worker’s income can buy twice as expensive a car. We draw one car for the French worker and another one—fancier and “twice as large”—for the American.

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What’s the problem? Well, first, people tend to respond to graphics by comparing areas. Because the larger car is twice as high and twice as long as the smaller one, its image has 4 times the area. Second, we are used to interpreting depth and perspective in drawings in terms of three-dimensional objects. Because the larger car is also, by implication, twice as wide as the smaller, it has 8 times the volume. The graphic can leave the subconscious impression that the U.S. worker has 8 times as much disposable income, instead of just twice as much. (Caution: Psychological studies show that the area perceived by a viewer does not exactly match the mathematical area.)

With these ideas in mind, evaluate—in a paragraph each—the data depictions in parts (a) through (c).