error_propagation

error_propagation - + ... + ( δc c ) 2 + ( δx x ) 2 + (...

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Summary of Rules for Error Propagation Suppose you measure some quantities a, b, c, . .. with uncertainties δa, δb, δc, . .. . Now you want to calculate some other quantity Q which depends on a and b and so forth. What is the uncertainty in Q ? The answer can get a little complicated, but it should be no surprise that the uncertainties δa, δb , etc. “propagate” to the uncertainty of Q . Here are some rules which you will occasionally need; all of them assume that the quantities a, b , etc. have errors which are uncorrelated and random . 1 1. Addition or subtraction: If Q = a + b + ... + c - ( x + y + ... + z ) then δQ = q ( δa ) 2 + ( δb ) 2 + ... + ( δc ) 2 + ( δx ) 2 + ( δy ) 2 + ... + ( δz ) 2 . 2. Multiplication or division: If Q = ab. ..c xy. ..z then δQ | Q | = s ( δa a ) 2 + ( δb b ) 2
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Unformatted text preview: + ... + ( δc c ) 2 + ( δx x ) 2 + ( δy y ) 2 + ... + ( δz z ) 2 . 3. Measured quantity times exact number: If A is known exactly (e.g. A = 2 or A = π ) and Q = Ax then δQ = | A | δx or equivalently δQ | Q | = δx | x | 4. Uncertainty in a power: If n is an exact number and Q = x n then δQ | Q | = | n | δx | x | . 5. General formula for error propagation: If Q = Q ( x ) is any function of x , then δQ = | dq dx | δx. 1 These rules can all be derived from the Gaussian equation for normally-distributed errors, but you are not expected to be able to derive them, merely to be able to use them. 1...
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This note was uploaded on 09/02/2010 for the course PHYS MERR1 taught by Professor Carter during the Spring '10 term at UMass (Amherst).

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