Math140: Statistics Outside Assignment 3: Distorting Numbers with Graphs As you have seen with histograms, graphs can be a great way to communicate information quickly and efficiently. But they can also be used to distort information and create false impressions. In this assignment, we will look at a couple of ways information can be distorted. One common trick is to play with the scale of the graph. If you look at the following table, it doesn’t look like the amount is changing all that much: Month $ in millions January $25.0 February $25.0 March $25.2 April $25.3 May $25.3 June $25.2 July $25.4 August $25.5 September $25.6 October $25.8 November $25.9 December $26.0 Here is a typical plot of the data: This particular plot was made using the defaults in Microsoft Excel. Notice the increase is quite obvious because the vertical scale is only a part of the total. We can exaggerate this by further restricting the scale and stretching the graph. Now the numbers are really taking off. Note the change in the vertical scale.Another common trick is to use some figure’s or icon’s size to represent size of a number. For example, we might use the size of a dollar bill to represent the cost of going to Wofford. We can draw two bills to show the change in tuition. Cost of Wofford in 2001 ($23,995) Cost of Wofford in 2007 ($37,655) Of course, there has been a very real increase in the cost of going to Wofford over the last six years, but the graph is deceptive. The width of the second bill has been increased by about half to indicate a 57% increase in tuition. But the height has also been increased by the same amount. The net effect is the area of the second bill is about 2 ½ times as large. The visual impact overstates the increase in tuition. Tuition hasn’t doubled. To Turn-in: Redraw each of theses graphs. For the first, draw the first graph with a vertical scale from $0 to $30. For the second, redraw the bills so the second bill is about 57% larger by total area. If you have software you are comfortable with, feel free to use it. Or you can use a sheet of graph paper or plan white paper. For the bills, you need only draw appropriately shaped rectangles, but you should maintain proportions so the shapes look like dollar bills. Explain how you determined the relative measurements of the