chapter6randomerror-全文預覽
【正文】 , (2) there is a symmetrical distribution of positive and negative deviations about the maximum, and (3) there is an exponential decrease in frequency as the magnitude of the deviations increases. Thus, small random uncertainties are observed much more often than very large ones. Areas under a Gaussian Curve It can be shown that, regardless of its width, % of the area beneath a Gaussian curve for a population of data lies within one standard deviation (?1?) of the mean ?. Thus, % of the data making up the population will lie within these bounds. Furthermore, approximately % of all data points are within ?2? of the mean and % within ?3?. Sample Standard Deviation Standard Deviation equation must be modified when it is applied to a small sample of data. Thus, the sample standard deviation s is given by the equation This equation differs from the standard deviation equation in two ways. First, the sample mean, x, appears in the numerator of sample standard deviation equation in place of the population mean, ?. Second, N in standard deviation equation is replaced by the number of degrees of freedom (N –1). The sample variance s2 is also of importance in statistical calculations. It is an estimate of the population variance ?2. ? ?? ?????? ?? ?x xNdNiiNiiN1 11 122_ Variance (s2) The standard deviation has the same units as the data, whereas the variance has the units of the data squared. It is easier to relate a measurement and its precision if they both have the same units. The advant
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