Ron Larson
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10.2 The Olympics

10.2 The Olympics
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  • 7. Describing Patterns in Women's 1000-Meter Speed Skating

    Describe any patterns in the graph. (See Example 3 and Example 4.)

    • Worked-Out Solution

      The winning time decreased every Olympics from 1960 through 1988. In 1992, it increased and then it decreased through 2002. Since 2002, it has increased at each Olympics.

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     _    _    _    _     ______   __   __    _____   
| || | || | || | ||  /_   _//  \ \\/ //  |__  //  
| || | || | || | ||    | ||     \ ` //     / //   
| \\_/ || | \\_/ ||   _| ||      | ||     / //__  
 \____//   \____//   /__//       |_||    /_____|| 
  `---`     `---`    `--`        `-`'    `-----`
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  • 8. Olympic Record in Women's 1000-Meter Speed Skating

    What is the Olympic record for the women's 1000-meter speed skating event? (See Example 3 and Example 4.)

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      ____     __   __  __    __     ___      _____   
 |  _ \\   \ \\/ // \ \\ / //   / _ \\   |__  //  
 | |_| ||   \ ` //   \ \/ //   | / \ ||    / //   
 | .  //     | ||     \  //    | \_/ ||   / //__  
 |_|\_\\     |_||      \//      \___//   /_____|| 
 `-` --`     `-`'       `       `---`    `-----`
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  • 9. Olympic Records in Women's 1000-Meter Speed Skating

    What percent of the winning times were Olympic records? (See Example 3 and Example 4.)

    • Worked-Out Solution

      There are 14 points in the graph. A point represents an Olympic record if no point to its left lies lower on the vertical axis. Count the number of points that represent Olympic records.

      Of the 14 times, 10 were Olympic records. So, the percent of winning times that were Olympic records is

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      _  __     ___       _____    _____    _    _   
 | |/ //   / _ \\    / ___//  |  ___|| | || | || 
 | ' //   | / \ ||   \___ \\  | ||__   | || | || 
 | . \\   | \_/ ||   /    //  | ||__   | \\_/ || 
 |_|\_\\   \___//   /____//   |_____||  \____//  
 `-` --`   `---`   `-----`    `-----`    `---`
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  • 10. Graphing Olympic Records in Women's 1000-Meter Speed Skating

    Sketch a graph that shows the Olympic record for each year in the data set. (See Example 3 and Example 4.)

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      _  _    _    _     _  _     ______    ____    
 | \| || | || | ||  | \| ||  /_   _//  |  _ \\  
 |  ' || | || | ||  |  ' ||   -| ||-   | |_| || 
 | .  || | \\_/ ||  | .  ||   _| ||_   | .  //  
 |_|\_||  \____//   |_|\_||  /_____//  |_|\_\\  
 `-` -`    `---`    `-` -`   `-----`   `-` --`
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  • 11. Finishing Times for Women's 1000-Meter Speed Skating

    Graphically represent the top 12 times for the 2010 Olympic women's 1000-meter speed skating event (shown in seconds). (See Example 4.)

    • Worked-Out Solution

      You can use a spreadsheet to make a bar graph of the top 12 times in the women's 1000-meter speed skating event at the 2010 Olympics.

      Another way to represent the data is by showing each speed skater in terms of time behind the winner. The stacked bar graph below illustrates the closeness of the top 12 times. Notice that all 12 speed skaters were within one second of winning.

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      _____      ___     ______    _    _     _  _   
 /  ___||   / _ \\  |      \\ | || | ||  | \| || 
| // __    / //\ \\ |  --  // | || | ||  |  ' || 
| \\_\ || |  ___  |||  --  \\ | \\_/ ||  | .  || 
 \____//  |_||  |_|||______//  \____//   |_|\_|| 
  `---`   `-`   `-` `------`    `---`    `-` -`
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  • 12. Men's 1000-Meter Speed Skating

    The winning times (in seconds) for the men's 1000-meter speed skating event are shown. Sketch a graph and describe any patterns. (See Example 3.)

    (1976, 79.32), (1980, 75.18), (1984, 75.80), (1988, 73.03), (1992, 74.85),

    (1994, 72.43), (1998, 70.64), (2002, 67.18), (2006, 68.90), (2010, 68.94)

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      _  __    _____               ______   ______   
 | |/ //  |  ___||     ___    /_   _// |      \\ 
 | ' //   | ||__      /   ||   -| ||-  |  --  // 
 | . \\   | ||__     | [] ||   _| ||_  |  --  \\ 
 |_|\_\\  |_____||    \__ ||  /_____// |______// 
 `-` --`  `-----`      -|_||  `-----`  `------`  
                        `-`
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