Graphics Interpretation Data Insights Practice Questions

This problem requires identifying branches that experienced an increase in variable costs from 7/2/2011 to 12/31/2011. These are the branches with a positive y-coordinate on the scatter plot. There are nine such branches above the x-axis. To find the median change in cost for the period beginning 1/1/2011 (the x-axis), we identify the middle value among these nine branches. The median is the 5th value when ordered from left to right. The median branch is located at approximately (-3.5, 19). The net variable cost for this branch over the entire year is the sum of the costs for each period (in thousands): -$3,500 + $19,000 = $15,500.

To find branches with a net decrease in costs it will help to understand what is represented by each quadrant. Quadrant I: these branches had an increase over both periods (3 branches) Quadrant II: these branches had a decrease during the first period but an increase during the second (6 branches) Quadrant III: these branches had a decrease during both periods (1 branch) Quadrant IV: these branches had an increase during the first period but a decrease during the second (5 branches) None of the branches that have an increase during both periods will have a net overall decrease, so we can ignore the branches in Quadrant I (3 branches). All branches that have a decrease during both periods will have a net overall decrease, so we count all branched in Quadrant III (1 branch). Now we must look at the more complicated situations – an increase in one period but a decrease in the other. To get a net overall decrease, we need a larger dollar decrease than increase. For Quadrant II (decrease in first period but increase in second), we need the X-coordinate (period 1) to be larger than the Y-coordinate (period). This appears to be the case for 3 points: (-7, 5.5), (-15.5, 5.5), and (-16, 0.5). Finally, for Quadrant IV (decrease in the second period but increase in the first), we need the Ycoordinate (period 2) to have larger magnitude than the X-coordinate (period 1). This appears to be the case for 3 points (2.5, -4.5), (0.5, -7.5), and (11, -17). For all these points, the decrease outweighs the increase. So in total, we have 1+3+3=7 branches out of the 15, a number slightly less than ½ or 50%. Plug it into the calculator to get 7/15 = 0.4667 = 47%. As an alternative, you could find all the points satisfying the expression x+y<0, or y<-x. Mentally sketch the downward-sloping line y=-x, which runs through the origin. What points fall below the line? You'll find 7 points there. From here, the final calculation is the same.

In order to compare the differences between pairs of countries, we begin by finding the approximate difference in 2008 cellular telephone subscribers between China and the US, and between the US and Italy. Using our eye as a guide for 2008 (the data point farthest to the right), we see that:

China – US = 650 – 275 = 375
US – Italy = 275 – 90 = 185

The question is asking us to find approximately what percent of the difference between China and the United States is made up by the difference between the United States and Italy. This translates to, "185 is approximately what percent of 375."

We solve this by simply doing (185 / 375) × 100 = 49.3%, which is approximately 50%.