74 CHAPTER 2 Exploring Data with Tables and Graphs A scatterplot can be very helpful in determining whether there is a correlation (or relationship) between the two variables. (This issue is discussed at length when the topic of correlation is considered in Section 10-1.) Correlation: Weighing Seals with a Camera EXAMPLE 1 Listed below are the overhead widths (cm) of seals measured from aerial photographs and the weights (kg) of these same seals (based on “Mass Estimation of Weddell Seals Using Techniques of Photogrammetry,” by R. Garrott of Montana State University). The purpose of the study was to determine if weights of seals could be determined from overhead photographs. Figure 2-14 is a scatterplot of the paired overhead width and weight measurements. The points show a distinct pattern of increasing values from left to right. This pattern suggests that there is a correlation between overhead widths and weights of seals. This suggests that we can “weigh” seals with a camera. Overhead Width 7.2 7.4 9.8 9.4 8.8 8.4 Weight 116 154 245 202 200 191 YOUR TURN. Do Exercise 7 “Cigarette Tar and Nicotine.” No Correlation: Heights of Presidents and Heights of their Main Opponents EXAMPLE 2 Data Set 22 in Appendix B includes heights (cm) of presidents and heights (cm) of their main opponents in the election. Figure 2-15 is a scatterplot of the paired heights. The points in Figure 2-15 do not show any obvious pattern, and this lack of a pattern suggests that there is no correlation between heights of presidents and heights of their opponents. YOUR TURN. Do Exercise 5 “Forecast and Actual Temperatures.” FIGURE 2-14 Overhead Widths and Weights of Seals Correlation: The distinct pattern of the plotted points suggests that there is a correlation between overhead widths and weights of seals. FIGURE 2-15 Heights of Presidents and Heights of Their Main Opponents No Correlation: The plotted points do not show a distinct pattern, so it appears that there is no correlation between heights of presidents and heights of their main opponents. Clusters and a Gap EXAMPLE 3 Consider the scatterplot in Figure 2-16. It depicts paired data consisting of the weight (grams) and year of manufacture for each of 72 pennies. This scatterplot shows two very distinct clusters separated by a gap, which can be explained by the inclusion of two different populations: Pre-1983 pennies are 97% copper A ti o Older and Younger Americans According to U.S. Census Bureau estimates, in 2035 there will be 76.7 million people age 18 and younger and there will be 78 million adults aged 65 or older. This would be the first time that the older Americans will outnumber the younger Americans. A U B e 2 b p
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