Question

In constructing a graph that compares average water usage per household in different communities, you choose to use cubes of different sizes. If the cubes are drawn so that their volumes are proportional to the volumes of water usage in different communities, is the resulting graph misleading? Why or why not?

A. No, using volume in graphs is never misleading.

B. Yes, using volume in graphs is always misleading.

C. Yes, the variable of interest is one-dimensional.

D. No, the variable of interest is three-dimensional.

Answer 1

D. No, the variable of interest is three-dimensional

Explanation:

The only choice that makes any sense here is the one shown above.

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However, a graph is necessarily a 2-dimensional presentation. So, your drawing of a cube, while potentially quite accurate, will be seen visually as occupying a certain area on the page. That is, it will be interpreted as though it were a 2-D object, rather than a 3-D object. The visual impact of a cube with volume 1³ = 1 and a cube with volume 3³ = 27 is more likely to be 1:9 than the desired 1:27, since the dimensions of the second cube will only be triple those of the first cube.

So, I would say, "Yes, the graph is likely to be misleading because the chosen presentation will not have the appropriate visual impact."

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The reason I would not choose (B) volume in graphs is always misleading is that graphs can be drawn in such a way that volume is appropriately represented.