Error_And_Uncertainty - PHYSICS 127 ERROR AND UNCERTAINTY...

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PHYSICS 127 ERROR AND UNCERTAINTY In Physics, like every other experimental science, one cannot make any measurement without having some degree of uncertainty. In reporting the results of an experiment, it is as essential to give the uncertainty, as it is to give the best-measured value. Thus it is necessary to learn the techniques for estimating this uncertainty. Although there are powerful formal tools for this, simple methods will suffice for us. To large extent, we emphasize a "common sense" approach based on asking ourselves just how much any measured quantity in our experiments could be in error. A frequent misconception is that the experimental error is the difference between our measurement and the accepted "official" value. What we mean by error is the estimate of the range of values within which the true value of a quantity is likely to lie. This range is determined from what we know about our lab instruments and methods. It is conventional to choose the error range as that which would comprise 68% of the results if we were to repeat the measurement a very large number of times. In fact, we seldom make the many repeated measurements, so the error is usually an estimate of this range. But note that the error range is established so as to include most of the likely outcomes, but not all. You might think of the process as a wager: pick the range so that if you bet on the outcome being within your error range, you will be right about 2/3 of the time. If you underestimate the error, you will lose money in your betting; if you overestimate it, no one will take your bet! Error: If we denote a quantity that is determined in an experiment as X, we can call the error X. Thus if X represents the length of a book measured with a meter stick we might say the length l = 25.1 ± 0.1 cm, where the central value for the length is 25.1 cm and the error, l is 0.1 cm. Both central value and error of measurements must be quoted in your lab writeups. Note that in this example, the central value is given with just three significant figures. Do not write significant figures beyond the first digit of the error on the quantity. Giving more precision to a value than this is misleading and irrelevant.
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