$$y = f(x_1, x_2, \ldots, x_N)$$

Equation 3 · Scientific Methods

How Scientific Instruments and Metrology Actually Work

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

The GUM’s central move is to treat every measured or estimated quantity a result depends on as a random variable with its own estimated standard uncertainty, and then to propagate those uncertainties through the mathematical relationship that produces the final result. If a measurement result y is a function of N input quantities, y = f($x_1$, $x_2$, $\ldots$, $x_N$) , the combined standard uncertainty is obtained from a first-order Taylor expansion of that function:

Meanings in this article

• $y$: the if a measurement result.

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Equation 3 · Scientific Methods

Comparing the Main Approaches to Scientific Instruments and Metrology

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Uncertainty itself has a standard grammar, laid out in the GUM and adopted domestically by NIST in Technical Note 1297. Every source of doubt about a measured value is classified as either a Type A evaluation — estimated from the statistical scatter of repeated observations — or a Type B evaluation — estimated from any other information, such as a calibration certificate, a manufacturer’s specification, or physical reasoning about a known systematic effect [ 2 ] [ 3 ] . These component uncertainties are combined, following an explicit propagation rule, into a combined standard uncertainty, which is then multiplied by a coverage factor (conventionally k=2 , corresponding loosely to a 95%…

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