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Aug 29, 2023 · Propagation of Error (or Propagation of Uncertainty) is defined as the effects on a function by a variable's uncertainty. It is a calculus derived statistical calculation designed to combine uncertainties from multiple variables to provide an accurate measurement of uncertainty.
Problem: Suppose you measure three numbers as follows: x = 200§2; y = 50§2; z = 40§2; where the three uncertainties are independent and random. Use step-by-step propagation to find the quantity q = x=(y ¡ z) with its uncertainty. Solution: Let D = y¡z = 10§2 p 2 = 10§3. Then q = x D = 20§20 p 0:012 +0:32 = 20§6: 10/5/01 7
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We can calculate the uncertainty propagation for the inverse tangent function as an example of using partial derivatives to propagate error. Define = (), where is the absolute uncertainty on our measurement of x.
Aug 27, 2020 · A propagation of uncertainty allows us to estimate the uncertainty in a result from the uncertainties in the measurements used to calculate that result. For the equations in this section we represent the result with the symbol R, and we represent the measurements with the symbols A, B, and C.
This section applies statistical methods to work out how errors in measured quantities affect the results of calculations. A related question is: how does uncertainty in the conditions affect a measurement (for example how do fluctuations in the temperature affect a rate constant measurement)?
This method relies on partial derivates from calculus to propagate measurement error through a calculation. As before we will only consider three types of operations: 1) multiplication/division/power functions, 2) addition/subtraction and 3) logarithmic/exponential functions.
Below we investigate how error propagates when mathematical operations are performed on two quantities x and y that comprise the desired quantity q. Addition and Subtraction. If we are trying to find the uncertainty, δq, associated with q = x + y, we can look at what the highest and lowest probable values would be.
