Linked Questions

9
votes
2answers
1k views

Is propagation of uncertainties linear?

I'm in doubt with one thing: let's imagine that we have $n+1$ quantities, $n$ of them being directly measured, and the other one being related to the first $n$ by a function $f : \mathbb{R}^n \to \...
4
votes
4answers
2k views

Why is the Pythagorean Theorem used for error calculation? [duplicate]

They say that if $A = X \times Y$, with $X$ statistically independent of $Y$, then $$\frac{\Delta{A}}{A}=\sqrt{ \left(\frac{\Delta{X}}{X}\right)^2 + \left(\frac{\Delta{Y}}{Y}\right)^2 }$$ I can't ...
2
votes
2answers
850 views

Formula for combining relative uncertainties [duplicate]

Different sources are giving me different formulae for combining relative uncertainties. One tells me to simply add the relative uncertainties together to get the combined uncertainty while another ...
2
votes
3answers
503 views

Want to prove a differentiation based formula for propagated uncertainty [duplicate]

I recently learned of the concept of propagated uncertainty, and I was introduced to the rule that if $$ X = AB$$ then if $A$ has an uncertainty of $\Delta A$ and $B$ has an uncertainty of $\Delta B$, ...
1
vote
0answers
211 views

Error propagation for products [duplicate]

Suppose you have two measured (independent) physical quantities $x$ and $y$ with relative errors $r_x := \frac{\delta x}{x}$ and $r_y := \frac{\delta y}{y}$, where $\delta x$ and $\delta y$ are the ...
0
votes
1answer
118 views

Propagation of uncertainty - which formula? [duplicate]

Can someone explain to me when do I use this formula ...and when do I use this one?
0
votes
1answer
97 views

Adding uncertainties when you cannot make any assumptions about the measurements [duplicate]

From what I read, when adding two $x$ and $y$ measurements with uncertainties $\delta x$ and $\delta y$, the resulting uncertainty is determined by doing: $$\delta z = \sqrt{(\delta x)^2 + (\delta y)^...
0
votes
0answers
46 views

Error Propagation: Why using derivatives instead of the function [duplicate]

Suppose I've measured the length $l$ with an uncertainty $\Delta l$ in order to calculate the Volume of a cube $V = l^3$. If I were to add an error: why am I supposed to do it like $\Delta V = \sqrt{\...
0
votes
2answers
25 views

What is the reasoning behind the rules for compounding errors? [duplicate]

There has to be a reason behind why we add fractional errors when the involved quantities are being multiplied or divided, or why, when converting units, do we have to divide the uncertainty with the ...
1
vote
2answers
246 views

Error propagation for cube and then square root [closed]

I have a variable $z$ and I know its error value $\Delta z$. So $z = 4.480$ and $\Delta z = 0.168$. I need to find $y + \Delta y$ such that $$y + \Delta y = (z+\Delta z)^{3/2}$$ So in this case, what ...
2
votes
1answer
61 views

Trouble with error propogation formulas for multiplication and exponentiation

In our lab notes, it states that for some relationship between variables of the form $Z=AB $, the errors are related by $$(\Delta Z /Z)^2=(\Delta A/A)^2 + (\Delta B /B)^2$$ And that for the relation ...
1
vote
0answers
47 views

A question about the propagation of uncertainties [duplicate]

If we have $f(x,y)=f(\overline{x}\pm\sigma_x,\overline{y}\pm\sigma_y)$ how is then $$\sigma_f=\sqrt{\left(\frac{\partial{f}}{\partial{x}}\right)^2\sigma_x^2+\left(\frac{\partial{f}}{\partial{y}}\right)...