Calculating error when constant is divided by variable

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Discussion Overview

The discussion revolves around calculating the uncertainty in a variable y when it is defined as a function of a constant k and a variable x, specifically in the context of the formula y = k/x. Participants explore how to propagate the uncertainty from x to y, considering different interpretations of "uncertainty."

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant asks how to calculate the uncertainty in y given the absolute uncertainty in x.
  • Another participant suggests that the relative uncertainty in y is the same as that in x.
  • A different participant questions the meaning of "uncertainty," asking whether it refers to standard deviation or a definite bound, and highlights the distinction between "absolute certainty" and "relative uncertainty."
  • Another response proposes using calculus to find dy/dx and substituting the uncertainty in x to propagate the error, noting that this method does not apply to combining two errors without knowledge of the error distribution.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of "uncertainty" and the methods for calculating it, indicating that multiple competing views remain without a consensus on the best approach.

Contextual Notes

There are unresolved questions regarding the definitions of uncertainty and the implications of different methods for error propagation, as well as the need for knowledge about error distributions when combining uncertainties.

akzo
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Hello everyone,

I have a very simple question but for some reason, I couldn't find the exact answer to it on the internet.
Let's say we have a formula y = k/x where k is constant and x and y are variables. Assume that I am given the absolute uncertainty in x how should I calculate the uncertainty in y?

Thanks in advance.
 
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The relative uncertainty on y is the same as the relative uncertainty on x.
 
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akzo said:
Assume that I am given the absolute uncertainty in x how should I calculate the uncertainty in y?

Are you using the term "uncertainty" to mean the standard deviation of a random variable? Or are you using "uncertainty" to mean a definite bound without any implication of a probability being involved? (For example, compare the different sets of "rules" given in notes: http://web.mit.edu/fluids-modules/www/exper_techniques/2.Propagation_of_Uncertaint.pdf rules 1&2 vs rules 3&4 )

Is the phrase "absolute certainty" used because you wish to distinguish it from "relative uncertainty" ?
 
If you know calculus, just calculate dy/dx and replace dx by your uncertainty in x. This is a general trick you can use to propagate an error through a function. It won't help you to combine two errors though. You need some knowledge of the error distribution for that.
 

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