The legendary story of William Tell, a master marksman, unfolds with a dramatic challenge imposed by a corrupt lord. Tell’s son faced execution unless William could shoot an apple off his head. While the original tale ends with William’s success, let’s explore two intriguing variations that highlight the concepts of accuracy and precision.
In this version, a bandit steals William’s reliable crossbow, forcing him to borrow a less accurate one from a peasant. This borrowed crossbow isn’t perfectly adjusted, causing William’s practice shots to cluster tightly below the bullseye. Fortunately, he has time to adjust his aim before the crucial moment.
In the second scenario, William begins to doubt his skills, and a tremor develops in his hand. His practice shots cluster around the apple but in a random pattern. Occasionally, he hits the apple, but the wobble introduces uncertainty, making a bullseye far from guaranteed. To save his son, William must steady his hand and regain confidence in his aim.
At the core of these variations are two terms often used interchangeably: accuracy and precision. However, their distinction is crucial in many scientific endeavors.
Accuracy refers to how close you come to the correct result. It improves with well-calibrated tools and proper training. In the story of the shaky hand, William’s shots were accurate, clustering around the correct result, but lacked precision.
Precision, on the other hand, is about consistency in achieving the same result using the same method. It improves with finely incremented tools that reduce estimation. The stolen crossbow scenario illustrates precision without accuracy, as William consistently hit the same wrong spot.
While low accuracy or precision might be acceptable in everyday tasks, engineers and researchers often require high levels of both. Factories and labs enhance precision through better equipment and detailed procedures, though these improvements can be costly. Managers must decide the acceptable level of uncertainty for each project.
Investments in precision can lead to groundbreaking achievements, such as space exploration. For instance, NASA’s Mars missions demonstrate the importance of accuracy and precision.
NASA doesn’t know the exact landing spot of their probes on Mars. Predicting the landing site involves extensive calculations based on measurements with inherent uncertainties. Factors like the Martian atmosphere’s density, the probe’s entry angle, and speed are considered. Computer simulations run thousands of scenarios, resulting in a landing ellipse that indicates the potential impact area.
In 1976, the Mars Viking Lander’s landing ellipse was 62 x 174 miles, nearly the size of New Jersey. This limitation forced NASA to avoid risky but intriguing landing sites. By 2012, advancements in technology and simulations reduced the Curiosity Lander’s landing ellipse to just 4 miles wide by 12 miles long, allowing NASA to target Gale Crater, a scientifically significant area.
While accuracy is the ultimate goal, precision reflects our ability to consistently achieve it. By understanding and applying these principles, we can aim for the stars with confidence, knowing we have the tools to hit our targets every time.
Imagine you are William Tell. Create a target with an apple drawn at the center. Use a rubber band and a paper clip to simulate a crossbow. Take turns with your classmates to aim and shoot at the apple from a set distance. Record where each shot lands. Discuss how accuracy and precision played a role in your attempts.
Set up a simple experiment using a ruler and a set of marbles. Drop the marbles from a fixed height onto a target on the floor. Measure how close each marble lands to the center of the target. Repeat the experiment several times. Analyze your results to understand the difference between accuracy (how close to the center) and precision (how close the marbles are to each other).
Rewrite the story of William Tell with a modern twist. Perhaps William is a scientist trying to land a probe on Mars. How do accuracy and precision play a role in his mission? Share your story with the class and discuss how these concepts are important in both the original tale and your modern version.
Use a computer simulation game that involves aiming and shooting, such as a virtual archery game. Pay attention to how the game measures your accuracy and precision. After playing, write a reflection on how the game helped you understand these concepts better.
Divide the class into two groups. One group will argue that accuracy is more important than precision, while the other group will argue the opposite. Use examples from the William Tell story and NASA’s Mars missions to support your arguments. After the debate, discuss how both accuracy and precision are crucial in different scenarios.
Accuracy – Accuracy refers to how close a measured value is to the actual or true value. – The accuracy of the thermometer was tested by comparing its readings to a known standard temperature.
Precision – Precision describes how close repeated measurements are to each other. – The precision of the scale was evident when it showed the same weight for the object multiple times.
Engineering – Engineering is the application of scientific and mathematical principles to design and build structures, machines, and systems. – The engineering team worked together to design a bridge that could withstand strong winds and heavy traffic.
Science – Science is the systematic study of the natural world through observation and experiment. – In science class, we learned about the water cycle and how it affects weather patterns.
Tools – Tools are instruments or devices used to perform tasks or measurements in scientific and engineering work. – Scientists use various tools, like microscopes and telescopes, to observe things that are too small or too far away to see with the naked eye.
Measurements – Measurements are the process of obtaining the size, quantity, or degree of something using standard units. – Accurate measurements are important in experiments to ensure reliable results.
Uncertainty – Uncertainty is the degree to which a measured value may vary from the true value. – When conducting experiments, scientists must account for uncertainty in their measurements to draw accurate conclusions.
Calculations – Calculations are mathematical processes used to determine a result or solve a problem. – The students performed calculations to find the speed of the car using the distance and time data they collected.
Technology – Technology refers to the use of scientific knowledge for practical purposes, especially in industry. – Advances in technology have made it possible to communicate instantly with people around the world.
NASA – NASA is the National Aeronautics and Space Administration, the United States government agency responsible for the nation’s civilian space program and for aeronautics and aerospace research. – NASA launched a new satellite to study the Earth’s climate and gather important data about global warming.