## Measurement Uncertainty Forum

### Is the true value of a measurand modeled by its population mean? Which one? mu(Y) or f(mu(X1), mu(X2),..., mu(Xn))?

Is the true value of a measurand modeled by its population mean? Which one? mu(Y) or f(mu(X1), mu(X2),..., mu(Xn))?

The aim of a measurement is to estimate the measurand true value and the respective uncertainty. When the measurand is obtained indirectly (through a functional relationship) what is the true value of the measurand? mu(Y) or f(mu(X1), mu(X2),..., mu(Xn))? Why?

Where:

Y = f(X1, X2,..., Xn)

Y is the measurand

f is the functional relationship

X1, X2,..., Xn are the input quantities

mu(*) is the population mean of *

If f(X1, X2,..., Xn) is a nonlinear function, then generally, mu(Y) is not equal to f(mu(X1), mu(X2),..., mu(Xn)) and if the true value of the measurand is mu(Y) then the approximation mu(Y) =~ f(mu(X1), mu(X2),..., mu(Xn)) is another source of uncertainty that is not considered in the GUM.

Thanks.