= Standard uncertainty
{title2=$u(x)$}
A <standard uncertainty> expresses a component of <measurement uncertainty> as an estimated <standard deviation>. It has the same <unit of measurement> as the <measurand>: $u(L)=0.2\,\mathrm{mm}$ describes a spread in a <length>, rather than a percentage or a known <measurement error>. A <Type A evaluation of uncertainty> uses statistical analysis of observations; a <Type B evaluation of uncertainty> uses other information, such as a reference certificate or instrument specification. These classify the evaluation method, not whether a physical effect is random or systematic.<Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results by Barry N. Taylor and Chris E. Kuyatt>[section 2: standard uncertainty and the A/B classification; Appendix D.1: error versus uncertainty]{ref}
For $n$ independent repeated readings with common <variance>, the <sample mean> has estimated <standard uncertainty> $s/\sqrt n$, where $s$ is their <sample standard deviation>. This is the <standard error> of the mean; the scatter $s$ instead describes individual readings. Repetition reduces this contribution, but a shared <measurement calibration> contribution remains. A quoted tolerance $\pm a$ supplies a different example: assigning a <continuous uniform distribution> within those bounds gives $u=a/\sqrt3$. That assignment is a model of the available information, not a consequence of repeating measurements.<Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results by Barry N. Taylor and Chris E. Kuyatt>[section 3: mean of independent observations; section 4.6: rectangular distribution]{ref}
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