In 1992, two UCLA professors compared the trends over time in male and female world records in several running events. Their data (in minutes) for the marathon, a race covering 42,195 meters, are in Table 2.17. Convert each of these times to velocity, in meters per minute, by dividing 42,195 meters by the time. Then plot the velocity data on a single time series graph, with the velocity axis running from 0 to 400 and the time axis running from 1900 to 2000. (Plot each point at the midpoint of the decade; for example, plot the 1910s data at 1915.) The professors wrote that,

“Despite the potential pitfalls, we could not resist extrapolating these record progressions into the future.” Draw one freehand straight line that fits the male data and another that fits the female data. Do these lines cross before 2000? Extrapolating the female line backward, what was the implied female world record in 1900?

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1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s Males Females 156.12 149.03 146.70 145.65 135.28 128.57 217.12 187.43 128.57 126.83 147.55 141.10