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If the instrument has a needle which points to a scale graduated in steps of 0.1 units, then depending on the design of the instrument, it is usually possible to estimate tenths between the successive marks on the scale, so it should be possible to read off the result to an accuracy of about 0.01 units.
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In industrial instrumentation, accuracy is the measurement tolerance, or transmission of the instrument and defines the limits of the errors made when the instrument is used in normal operating conditions. [7] Ideally a measurement device is both accurate and precise, with measurements all close to and tightly clustered around the true value.
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 ...
The statistical errors, on the other hand, are independent, and their sum within the random sample is almost surely not zero. One can standardize statistical errors (especially of a normal distribution ) in a z-score (or "standard score"), and standardize residuals in a t -statistic , or more generally studentized residuals .
In most indicating instruments, the accuracy is guaranteed to a certain percentage of full-scale reading. The limits of these deviations from the specified values are known as limiting errors or guarantee errors. [6]
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.