68 CHAPTER 2 Exploring Data with Tables and Graphs Pictographs Drawings of objects, called pictographs, are often misleading. Data that are one- dimensional in nature (such as budget amounts) are often depicted with two-dimensional objects (such as dollar bills) or three-dimensional objects (such as stacks of dollar bills). By using pictographs, artists can create false impressions that grossly distort differences by using these simple principles of basic geometry: (1) When you double each side of a square, its area doesn’t merely double; it increases by a factor of four. (2) When you double each side of a cube, its volume doesn’t merely double; it increases by a factor of eight. FIGURE 2-12 Nausea in a Clinical Trial (a) (b) PICTOGRAPHS When examining data depicted with a pictograph, determine whether the graph is misleading because objects of area or volume are used to depict amounts that are actually one-dimensional. (Histograms and bar charts represent one-dimensional data with two-dimensional bars, but they use bars with the same width so that the graph is not misleading.) Pictograph of U.S. Phone Records Collected EXAMPLE 9 In two recent and consecutive years, the number of phone records collected by the U.S. National Security Agency jumped from 151 million to 534 million, and 534 million is roughly 3.5 times 151 million. Refer to Figure 2-13 and see that the larger phone is about 3.5 times as tall and 3.5 times as wide as the smaller phone. The larger phone appears to be about 12 times as large as the smaller phone, but it should be only 3.5 times as large as the smaller phone. (Brief explanation: If you double the sides of a square, the area becomes four times as large.) Figure 2-13 therefore misleads readers into thinking that the increase is dramatically more substantial than it really is. A better graph would be a simple bar chart (vertical scale starting at zero) with two bars for the two years. YOUR TURN. Do Exercise 19 “Cost of Giving Birth.” Year 1 - 151 million Year 2 -534 million FIGURE 2-13 Pictograph of U.S. National Security Agency Collected Phone Records
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