Question

in a particular county the average homeowner owns 0.27 acres of land while in a neighboring county the average homeowner owns 0.54 acres of land. does the graph depict the data fairly? 0.27 acres 0.54 acres county neighboring county (1 point) yes, the area of the box depicting the county average is smaller than the area of the box depicting the neighboring county average. yes, the area of the box depicting the county average is proportional to the area of the box depicting the neighboring county average. no, the length of the box depicting the county average should be proportional to the length of the box depicting the neighboring county average. no, the area of the box depicting the county average should be proportional to the area of the box depicting the neighboring county average.

Explanation:

Step1: Analyze the ratio of the areas

The ratio of the land - ownership amounts is $\frac{0.27}{0.54}=\frac{1}{2}$. For a fair graph, if we assume the shapes are similar (say rectangles), the ratio of the areas of the two shapes representing the data should be in the same ratio as the data values. Let the first rectangle have area $A_1$ and the second have area $A_2$. We want $\frac{A_1}{A_2}=\frac{0.27}{0.54}$.

Step2: Check the graph visually

If we assume the rectangles are similar, and we consider the area of a rectangle as $A = l\times w$. Just looking at the graph, we can see that the area of the rectangle representing 0.54 acres is not twice the area of the rectangle representing 0.27 acres. The area of a rectangle should be proportional to the value it represents.

Answer:

D. No, the area of the box depicting the county average should be proportional to the area of the box depicting the neighboring county average.