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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.
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 ...
Uncertainty of a measurement can be determined by repeating a measurement to arrive at an estimate of the standard deviation of the values. Then, any single value has an uncertainty equal to the standard deviation.
Standard errors provide simple measures of uncertainty in a value and are often used because: ... whereas the standard deviation of the sample is the degree to which ...
Standard deviation may serve as a measure of uncertainty. In physical science, for example, the reported standard deviation of a group of repeated measurements gives the precision of those measurements. When deciding whether measurements agree with a theoretical prediction, the standard deviation of those measurements is of crucial importance ...
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The variances (or standard deviations) and the biases are not the same thing. To illustrate this calculation, consider the simulation results from Figure 2. Here, only the time measurement was presumed to have random variation, and the standard deviation used for it was 0.03 seconds. Thus, using Eq(17),
That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. [1] [2] Risk measures typically quantify the downside risk, whereas the standard deviation (an example of a deviation risk measure) measures both the upside and downside risk