The outcome of an analytical measurement (application of the chemical measurement process), or value attributed to a measurand. This may be the result of direct observation, but more commonly it is given as a statistical estimate derived from a set of observations. The distribution of such estimates (estimator distribution) characterizes the chemical measurement process, in contrast to a particular estimate, which constitutes an experimental result. Additional characteristics become evident if we represent $\hat{x}$ as follows: $$\begin{array}{ccccc}& & & e& \\ & & & ⎴⎴⎴& \\ \hat{x}=\tau +e=& \tau & +& \mathrm{\Delta }& +& \delta & =\mu +\delta \\ & ⎵⎵⎵& & & \\ & \mu & & & \end{array}$$ The true value, $\tau$, is the value $x$ that would result if the chemical measurement process were error-free. The error, $e$, is the difference between an observed (estimated) value and the true value; i.e. $e=\hat{x}-\tau$ (signed quantity). The total error generally has two components, bias ($\mathit{\Delta }$) and random error ($\delta$), as indicated above. The limiting mean, $\mu$, is the asymptotic value or population mean of the distribution that characterizes the measured quantity; the value that is approached as the number of observations approaches infinity. Modern statistical terminology labels this quantity the expectation value or expected value, $E(\hat{x})$. The bias, $\mathit{\Delta }$, is the difference between the limiting mean and the true value; i.e. $\mathit{\Delta }=\mu -\tau$ (signed quantity). The random error, $\delta$, is the difference between an observed value and the limiting mean; i.e. $\delta =\hat{x}-\mu$ (signed quantity).