# Combining Uncertainties - Mean

1. Apr 20, 2009

### crankine

1. The problem statement, all variables and given/known data
How do I combine the uncertainties to get a mean value±error?

Okay I know I have huge errors and if anyone could suggest what's wrong (I have huge errors in strain because the changes in length were tiny and the calibration errors were of the same order) thats great but my main problem is:

These are my results in GPa from a youngs modulus experiment. How do I combine the uncertainties to get a mean value±error?

97.6±27.1
95.2±67.1
125.5±41.4
192.1 (Negligible error)
154.1 (Negligible error)
95.8±30.9
95.8±25.5
110.5±24.8

2. Relevant equations

3. The attempt at a solution
I've taken the mean of the first part = 120.8

On the internet people seem to be saying things like
"If more than 10 but fewer than 50 trials have been taken, report the uncertainty as the
average of the absolute values of the deviations of the individual values."
In that case its ±36.1

But someone told me to use the Pythagorean combining formula which I thought might be wrong...
±95.8 nearly 3/4 of my actual value.

P.S How many significant figures do you round off to if the uncertainty is greater than 1?!
if it was ±0.0002556 then it would be ±0.0003, fine, but does ±27.1 become ±30?

by the way that quote was from http://cc.ysu.edu/~jeclymer/Uncertainty%20Tutorial.pdf [Broken]
page 4

Last edited by a moderator: May 4, 2017