One of the course texts, An Introduction to Error Analysis by John R. Taylor, provides a thorough, easy-to-read introduction to the analysis of uncertainties (errors) in physical measurements. You should read at least the first four chapters by Tuesday, September 14, and take the companion quizzes on WebQuiz. You must retake the quizzes until you have mastered this material. If you get stuck and have questions, please ask us.
Whenever we measure a quantity such as a length, a mass, a time, a current, a velocity, etc., the measurement is inevitably inexact. Imagine shooting a ball from a spring-loaded projectile launcher and marking the distance horizontal distance traveled by the ball in flight. You would probably not be surprised if the ball didn't land at exactly the same spot if you repeated the experiment, doing your best to keep all the launch conditions exactly the same. If the distance traveled on the second flight was 1 cm less than the 2 m of the first flight, you would probably find that reasonable.
On the other hand, you undoubtedly would be surprised if on the second launch the ball flew twice as far, although there are some experiments where an analogous change in the results would not be unreasonable.
Frequently it isn't "good enough" to know about where the projectile will land. You will need to know how to locate the most probable landing position, and how rapidly the likelihood falls of with distance as you move from this most probable position. You might determine, for example, that the ball will land with a probability of about two-thirds within a 1-cm-radius spot centered at a certain position, and that it will land with 95% certainty in a 2-cm-radius spot centered at the same place. If this is acceptable to your experiment or project, you will move on. If not, you will need to reduce the uncertainty in the landing position by analyzing the causes of that uncertainty and modifying your apparatus or procedure to minimize them.
Updated 8/14/99 by Peter N. Saeta .