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Equation 4 · Part 14 · Comparing the Main Approaches to Scientific Instruments and Metrology

Ending index or upper bound: N

uc2(y)=∑i=1N(∂f∂xi)2u2(xi)u_c^2(y) = \sum_{i=1}^{N} \left( \frac{\partial f}{\partial x_i} \right)^2 u^2(x_i)
NN

What this part means

This label says where the repeated addition, multiplication, or accumulation stops. It sets the last term or end of the range.

Its job in the formula

N appears in the bound of this sum. The bound states where the repeated operation starts, ends, or which values it includes.

The passage around this formula

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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Learn the underlying idea

Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.