Lab1 - Lab 1 I.3.1 Error Analysis Introduction Physical...

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Lab 1 Error Analysis I.3.1 Introduction Physical quantities, length, mass, time, etc., are constantly being measured in the laboratory. All experimentally determined quantities contain some degree of error or uncertainty. It is important that the experimentalist knows how to record the data and results so that it’s clear just how precise the data is, and is familiar with the various sorts of error. 1.3.2 Types of Error A. Systematic or constant errors : These errors result from using an instrument that is not calibrated properly. For example, using a meter stick that is actually shorter in length than a meter or using a voltmeter, which has not been “zeroed”, would result in a systematic error being introduced into the experiment. Corrections can be made to the data to compensate for systematic errors if the type and extent of the error is known. Students should always be aware that systematic errors may exist and each lab report should contain a statement concerning possible sources of systematic error in the experiment. B. Random errors : These errors result from fluctuations of such parameters as temperature, pressure, humidity, line voltage, or magnetic and electrical interference which cause repeated measurements to disagree. In addition, most instruments require an estimate of the fraction of smallest scale division and the observer's estimate may vary from measurement to measurement. Most lab reports will require an estimate of the random error in measurements made. C. Human errors : These errors are caused by outright mistakes in reading instruments, performing the experiment, or recording data. Included in this category are mistakes made in calculations. Fortunately, these errors are usually apparent either as obviously incorrect data points or as results, which are not reasonably close to the expected results. These kinds of errors wreck your experiment and /or the lab report. It’s really good to avoid these. 11
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1.3.3 Estimating Random Error The amount of uncertainty associated with a quantity, which has been measured “n” number of times, is estimated by calculating the mean and its standard error . No estimate of the random error can be deduced from only a single measurement! The arithmetic mean, x , (or average) of a series of n measurements ( x i ) is defined by: (1) The standard deviation of the quantities x are obtained by the following formula: σ x = 1 n - 1 ( x - x i ) 2 Σ i =1 n (2) The standard deviation of the mean or "standard error", σ x , is then: σ x = σ x n (3) Observe that the above formula for σ x with n-1 in the denominator is the correct expression for the sample standard deviation when the mean is not known exactly. However, some calculators with a standard deviation key use a different definition of
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This note was uploaded on 10/15/2011 for the course PHYSICS 0207239 taught by Professor Mamar during the Spring '09 term at Jordan University of Science & Tech.

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Lab1 - Lab 1 I.3.1 Error Analysis Introduction Physical...

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