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10.3–10.4 Quiz

10.3–10.4 Quiz
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  • 1. Identifying and Estimating Missing Data

    The chart shows the average absolute change in win percentage for all the teams in a league for each season shown. For instance, the value for the NBA in 2007 is based on the average absolute change in win percentages between the 2006-2007 season and the 2007-2008 season.

    Identify and estimate any missing data points.

    • Worked-Out Solution

      There is a data point missing for the NHL in 2004. Drawing a straight line between the values for 2003 and 2005, you can estimate that the value is 0.08.

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     _    _     _____    _    _    _    _      _____  
    | || | ||  |  ___|| | \  / || | || | ||   / ___// 
    | || | ||  | ||__   |  \/  || | || | ||   \___ \\ 
    | \\_/ ||  | ||__   | .  . || | \\_/ ||   /    // 
     \____//   |_____|| |_|\/|_||  \____//   /____//  
      `---`    `-----`  `-`  `-`    `---`   `-----`   
                                                      
    
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  • 2. Determining the League with the Most Competitive Balance

    The chart shows the average absolute change in win percentage for all the teams in a league for each season shown. For instance, the value for the NBA in 2007 is based on the average absolute change in win percentages between the 2006-2007 season and the 2007-2008 season.

    Which major sports league has the most competitive balance? Explain your reasoning.

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                 ___    __    __    _____     ______  
        ___     / _ \\  \ \\ / //  |  ___||  /_____// 
       /   ||  / //\ \\  \ \/ //   | ||__    `____ `  
      | [] || |  ___  ||  \  //    | ||__    /___//   
       \__ || |_||  |_||   \//     |_____||  `__ `    
        -|_|| `-`   `-`     `      `-----`   /_//     
         `-`                                 `-`      
    
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  • 3. Estimating Future Data

    The chart shows the average absolute change in win percentage for all the teams in a league for each season shown. For instance, the value for the NBA in 2007 is based on the average absolute change in win percentages between the 2006-2007 season and the 2007-2008 season.

    In the 2009-2010 season, an NBA team won 50 out of 82 games. How many games would you expect the team to win in the 2010-2011 season?

    • Worked-Out Solution

      The average NBA team's win percentage varies by about 0.10 every year. In the 2009-2010 season, the team's win percentage was about 0.61.

      So, next year you would expect the team's win percentage to be in the range 0.61 ± 0.10, or from 0.51 to 0.71. This means that you would expect the team to win from 0.51(82) ≈ 42 to 0.72(82) ≈ 58 games.

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      ______   __   __   ______    _    _    _    _   
     /_____//  \ \\/ // |      \\ | || | || | |  | || 
     `____ `    \ ` //  |  --  // | || | || | |/\| || 
     /___//      | ||   |  --  \\ | \\_/ || |  /\  || 
     `__ `       |_||   |______//  \____//  |_// \_|| 
     /_//        `-`'   `------`    `---`   `-`   `-` 
     `-`                                              
    
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  • 4. Bad Sports Teams

    The chart shows the average absolute change in win percentage for all the teams in a league for each season shown. For instance, the value for the NBA in 2007 is based on the average absolute change in win percentages between the 2006-2007 season and the 2007-2008 season.

    Do you agree with the following comment? Use the chart to explain your reasoning.

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      _____     _____     ______     ___      _____   
     |__  //   |  ___||  /_   _//   / _ \\   |__  //  
       / //    | ||__      | ||    | / \ ||    / //   
      / //__   | ||__     _| ||    | \_/ ||   / //__  
     /_____||  |_____||  /__//      \___//   /_____|| 
     `-----`   `-----`   `--`       `---`    `-----`  
                                                      
    
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  • 5. Frostbite Risk while Camping

    Use the chart to identify the frostbite risk for camping in -15°F weather with a 20 mph wind.

    • Worked-Out Solution

      From the graph, you can see that -15°F weather and 20 mph wind means that there is danger of frostbite.

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      _____     _____   __    __     ___      _____   
     / ____||  |  ___|| \ \\ / //   / _ \\   / ____|| 
    / //---`'  | ||__    \ \/ //   | / \ || / //---`' 
    \ \\___    | ||__     \  //    | \_/ || \ \\___   
     \_____||  |_____||    \//      \___//   \_____|| 
      `----`   `-----`      `       `---`     `----`  
                                                      
    
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  • 6. Frostbite Risk while Hiking

    Use the chart to identify the frostbite risk for hiking in 0°F weather with a 5 mph wind.

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      ______   _    _     ______   __   __   __   _   
     /_____// | || | ||  /_   _//  \ \\/ // | || | || 
     `____ `  | || | ||  `-| |,-    \ ` //  | '--' || 
     /___//   | \\_/ ||    | ||      | ||   | .--. || 
     `__ `     \____//     |_||      |_||   |_|| |_|| 
     /_//       `---`      `-`'      `-`'   `-`  `-`  
     `-`                                              
    
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  • 7. Frostbite Risk while Skiing

    Use the chart to identify the frostbite risk for skiing in -30°F with a 25 mph wind.

    • Worked-Out Solution

      From the graph, you can see that -30°F weather and 25 mph wind means that there is extreme danger of frostbite.

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      ______     ___      ______   __   __    _____   
     /_   _//   / _ \\   /_   _//  \ \\/ //  |__  //  
       | ||    | / \ ||  `-| |,-    \ ` //     / //   
      _| ||    | \_/ ||    | ||      | ||     / //__  
     /__//      \___//     |_||      |_||    /_____|| 
     `--`       `---`      `-`'      `-`'    `-----`  
                                                      
    
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  • 8. Frostbite Risk while Climbing

    Use the chart to identify the frostbite risk for climbing in -25°F weather with a 10 mph wind.

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     _    _      ___       _____    _____    __   __  
    | |  | ||   / _ \\    / ___//  |  ___||  \ \\/ // 
    | |/\| ||  | / \ ||   \___ \\  | ||__     \   //  
    |  /\  ||  | \_/ ||   /    //  | ||__     / . \\  
    |_// \_||   \___//   /____//   |_____||  /_//\_\\ 
    `-`   `-`   `---`   `-----`    `-----`   `-`  --` 
                                                      
    
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