Type A evaluation of uncertainty is the estimation of variance of the data obtained by direct measurements.(Type A Uncertainty) Normal statistical method of finding the mean and square of its deviations from the observation is used to estimate the variance. If the number of observed values of the input quantity Xp is np, then the degree of freedom is np 1. Each input estimate of xp and its variance is obtained from a distribution of possible values of the input quantity Xp. This probability distribution is frequency based, that is based on a series of observation xp;q of Xp. The Type A evaluation is based on the frequency distribution, which, in most cases, is the normal (Gaussian) distribution. In case of dependent input quantities, covariances are also estimated.

In most cases, the best available estimate or the expected value of a quantity Xp that varies randomly is the arithmetic mean of several corrected observations of this quantity. That is

Here np is the number of corrected observations taken under similar conditions. Individual observation xp;q may differ in value because of random variations in the influence quantities or any other random effect. The variance of observations, which is the best estimate of variance2 – the variance of the probability distribution of quantity Xp, is obtained from

The positive square root of s2.xp/ is the standard uncertainty uA.xp/ determined by Type A evaluation method of uncertainty. The symbol uA stands for uncertainty arrived at by Type A evaluation.

Source: measurement uncertainty