Equation 3 · Part 1 · How Scientific Instruments and Metrology Actually Work

Symbol y

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

y

What this part means

the if a measurement result.

Its job in the formula

y is part of the quantity the equation computes from the expression on the right.

Full expressionSymbol yArticle meaning

Where the article explains it

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:

The passage around this formula

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:

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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