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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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