Measurement Error Normal Distribution
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for accurately describing the nature of measurement distributions. In practice, one must deal with a finite set of values, so the nature of their distribution is never known precisely. As always, one
Gaussian Distribution Error Function
proceeds on the basis of reasonable assumptions. Consider a large number of repeated measured normal distribution of errors values of a physical quantity. Suppose the number of values is very large, and a bar graph (Fig. 5.1) is made gaussian and normal error distribution pdf of the number of occurrences of each value. The tops of the bars are connected with a smooth curve. Such a curve is called an error distribution curve. Such curves come in an infinite variety
Error Distribution Definition
of shapes, as the four examples in Fig. 5.1 illustrate. Bar graph representationof an error distribution. A bimodal distribution. A distribution with a flattened top. Gaussian (normal) distribution very accurately drawn from computer generated data. Fig. 5.1 Error distributions. One can often guess the shape of the curve, even with a finite set of values, especially such features as symmetry and spread. Just as we represent a set of
Normal Distribution Of Errors Regression
values by one value (some kind of average), so also we can represent the shape of the distribution curves by measures of dispersion (spread), skewness, etc. We can describe the measurement and its uncertainty by just a few numbers. The mathematical discipline of statistics has developed systematic ways to do this. 5.2 MEASURES OF CENTRAL TENDENCY OF DATA Some of the "measures of central tendency" commonly used are listed here for reference: ARITHMETIC MEAN. (or simply the MEAN, or the AVERAGE): The sum of the measurements divided by the number of measurements. GEOMETRIC MEAN. The nth root of the product of n positive measurements. HARMONIC MEAN. The reciprocal of the average of the reciprocals of the measurements. MEDIAN. The middle value of a set of measurements ranked in numerical order. MODE The most frequent value in a set of measurements. (more precisely: the value at which the peak of the distribution curve occurs.) 5.3 MEASURES OF DISPERSION OF DATA The difference between a measurement and the mean of its distribution is called the DEVIATION (or VARIATION) of that measurement. Measures of dispersion are defined in terms of the deviations. Some commonly used measures of dispersion are listed for reference: AVERAGE DEVIATION FROM THE MEAN. (usually just AVE
measured values around their average is approximately normal. Often, in fact, the random experimental https://www.roma1.infn.it/~dagos/cern/node58.html error , which causes the fluctuations of the measured values around the unknown true value of the physical quantity, can be seen as an incoherent sum of smaller contributions (4.79) each contribution having a distribution which satisfies the conditions of the central limit theorem. Giulio D'Agostini 2003-05-15
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