Can uncertainties become smaller in certain cases?

[kodek64]

(First post. Go easy on me, mods :D)
EDIT: Seems I got the wrong forum. If a mod could be so kind to move it, I'd appreciate it :P

Hi everyone!

I'm working on a formal lab report for my physics class, and after propagating my uncertainties into a formula, I got an even smaller uncertainty relative to the original uncertainties (one of the indep. variables was 9% while my propagated uncertainty was 6%)

Is this possible in ANY case?

If it's not, I will post more information about the equations I'm using. I already spent 2 hours looking at all the numbers and using mathematica to calculate the results for me, and I just don't know what could be wrong with it (if there's even anything wrong with it).

Thanks for your help,

KodeK

 

[mathman]

Is this possible in ANY case?

Yes. In general if the random variables are independent, the uncertainties tend to smooth out.

 

[kodek64]

Yes. In general if the random variables are independent, the uncertainties tend to smooth out.

Hmm, I'd like to show you the equations I'm using just to get an okay so I know I'm doing this right. How would I copy mathematica's LaTeX output and paste it on the site? I don't want to have to copy an in-line equation :P

 

[kodek64]

Here's a screenshot of the problem I'm having:

http://img517.imageshack.us/img517/9827/physicslabhelpii0.jpg

 

[Count Iblis]

Yes, the errors can become less if the derivatives are small. If you evaluate a function f of independent variables x1, x2, ..., with respective errors dx1, dx2, ..., then the error in f is:

df = sqrt[df1^2 + df2^2 + ...]

where

df1 = f(x1 + dx1/2, x2,...) - f(x1 - dx1/2, x2,...)


df2 = f(x1, x2+dx2/2,...) - f(x1, x2 - dx2/2,...)

etc.