# Propagation of uncertainty

1. May 12, 2012

### Gavroy

hi

i have some measured values that refer to a simple experiment where a stone was thrown along a fixed length and now i have these values for the time the stone needed

time 13.8 13.7 13.9 13.5 14.4 14.6 14.1 14.3 13.9 14.7

i was asked to explain how many decimal places one would write down when one determines the mean value of this set?

well, i guess it is only one, as none would be pretty uncertain and more than one would be pointless.
but then i was also asked, how many values i would need(these are 10) in order to be able to write down another decimal place and also how many values i would need to write down a third decimal place and so on. is there any rule or does anybody here have an idea what an appropriate number might be?

2. May 12, 2012

### dikmikkel

Propagnation of uncertainty? maybe it is a purely statistical question so:
Another consideration is the standard deviation i get: $\sigma = 0.4$
So maybe you need to specify 0 decimals because of the SD, but it can be calculated more precisly:
You need to assume that the time measurements follows a distribution, maybe normal-dist.?
The max error E in a Standard-normal distribution is given by:
$E = z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$
where n is the number of measurements and alpha is the significance(by standard 5%).

Last edited: May 12, 2012
3. May 12, 2012

### Gavroy

sorry, that i maybe misunderstand you, but are you saying that if the standard error is less than 0.1 one can write down the mean value with one more decimal place and if it is less than 0.01 one can write down another decimal place? or where would you draw the line?