Calculating Errors: Adding, Subtracting, Multiplying & More

[Pixter]

Just want to get a straight answear if possible..

How dou you add different types of errors.


lets say I have and length error of 2 +-1 and another of 5+-2

what happens to the error when I add/subtract...multiply/divide...square/sqrt ?

then If I have and length error of 2+-1 and a mass error of 20+-1 and first I change the absolut error to percentage, and then what happens when I:
add/subtract...multiply/divide...square/sqrt ?

Doing lot's of labs and just need some clarification on this..

would be nice if someone could show how to with these examples... thanks a lot guys & girls

 

[teknodude]

personaly i think error analysis is a real pain to calculate sometimes, cause you have to carry over all the +- uncertainties.

try this link

http://www.smccd.net/accounts/goodman/physics/p270/p270_labhandouts/unknown_mass.pdf

read pages 2-4. Once you do the practice problem on page 4, you should be good to go.

 

[ahrkron]

Just be careful with this, since the formulas given correspond to the case of using absolute deviations to express the errors. More often, people use standard deviations, in which case the errors are combined differently (for addition, subtraction and product, the relative uncertainties are added in quadrature).

This may help to clarify the difference: http://www.rit.edu/~uphysics/uncertainties/Uncertaintiespart2.html#addsub

 

[Warr]

To explain the difference between using absolute deviations and standard deviations, let's just say that by using absolute deviations, you assume the worst case scenario. Since data usually is distributed (as as such, errors), it therefore must be partially governed by a stardard deviation. Hence being added in a quardrature gives the uncertainty from a probablistic point of view.