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The mean and the standard deviation of a set of data are descriptive statistics usually reported together. In a certain sense, the standard deviation is a "natural" measure of statistical dispersion if the center of the data is measured about the mean. This is because the standard deviation from the mean is smaller than from any other point.
If the considered function is the density of a normal distribution of the form = [()] where σ is the standard deviation and x 0 is the expected value, then the relationship between FWHM and the standard deviation is [1] = .
Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. For instance, when the variance of data in a set is large, the data is widely scattered. On the other hand, when the variance is small, the data in the set is clustered.
In metrology, measurement uncertainty is the expression of the statistical dispersion of the values attributed to a quantity measured on an interval or ratio scale.. All measurements are subject to uncertainty and a measurement result is complete only when it is accompanied by a statement of the associated uncertainty, such as the standard deviation.
The second standard deviation from the mean in a normal distribution encompasses a larger portion of the data, covering approximately 95% of the observations. Standard deviation is a widely used measure of the spread or dispersion of a dataset. It quantifies the average amount of variation or deviation of individual data points from the mean of ...
σ g: Geometric standard deviation. This value is determined mathematically by the equation: σ g = D 84.13 /D 50 = D 50 /D 15.87. The value of σ g determines the slope of the least-squares regression curve. α: Relative standard deviation or degree of polydispersity. This value is also determined mathematically.
In these examples, we will take the values given as the entire population of values. The data set [100, 100, 100] has a population standard deviation of 0 and a coefficient of variation of 0 / 100 = 0; The data set [90, 100, 110] has a population standard deviation of 8.16 and a coefficient of variation of 8.16 / 100 = 0.0816
Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...