The result of a measurement is an estimate of the measurand and is incomplete unless it is accompanied by a quantitative estimate of its uncertainty.
In accordance with the Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results (Taylor and Kuyatt, 1994), estimates of uncertainty are classified into two categories, “Type-A” (evaluated by statistical methods) and “Type-B” (evaluated by other means). Uncertainty classification differs from the classification of error as either random or systematic because either type of uncertainty can apply to either type of error. For example, a component in an analysis of uncertainty may be the uncertainty in calibration, for which one component is the estimate that arises from the standard deviation of the calibration data about the calibration curve. This is a Type-A evaluation of an assumed random error in the calibration process, but the resulting uncertainty applies to the systematic error resulting from use of the calibration.
where x̄ is the mean of the N measurements xi. The measurement would be reported as x̄ ± u and the degrees of freedom would be reported as v = N-1.