A study is conducted to compare the average square footage of homes in different communities. If squares are drawn so that their areas are in proportion to the average square footage, is the resulting graph misleading? Why or why not?

A.No, using areas in graphs is never misleading.
B.No, the variable of interest is two-dimensional.
C.Yes, using areas in graphs is always misleading.
D.Yes, the variable of interest is two-dimensional.

Question

A study is conducted to compare the average square footage of homes in different communities. If squares are drawn so that their areas are in proportion to the average square footage, is the resulting graph misleading? Why or why not?
 	
	A.No, using areas in graphs is never misleading.
	B.No, the variable of interest is two-dimensional.
	C.Yes, using areas in graphs is always misleading.
	D.Yes, the variable of interest is two-dimensional.

anonymous · Answer

Friend, first, you can rule out options "A" and "C". Clearly the use of the words "never" and "always" is not accurate. That leaves the other two options. When I have trouble with a math problem, I tray to solve an easier version of the problem, then come back to the problem I want to solve. What if there were only 3 communities in the study with mean home sizes 1000, 2000 and 3000 square feet, call them C1, C2 and C3 respectively.

anonymous · Answer

What would our graph look like? It would have three squares The C2 square would be twice as big as the C1 square, and the C3 square in the graph would be three times as big as the C1 square. Why? Because the problem says that the square in the graph are proportional. By definition, that is exactly how proportional the average home sizes are. 2000 is two the area of 1000, and 3000 is three times the area of 1000. So, is this graph accurate or misleading?