How is uncertainty affected by absolute numbers?

[legends784]

Example:
Say I want to calculate the evaporation rate of water and so I record the mass of some amount of water every 30 seconds for 5 minutes. The uncertainty in the scale is inherently .0001g and so that would be the uncertainty in the mass of any individual measurement, but how would I calculate the uncertainty for what I am actually looking for which is a rate. I.e by finding the difference between each concurrent measurement, dividing it by 30seconds, then adding up each of the individual rates in g/s and calculating an average rate in mg/min.

I can't physically wrap my head around how the error transfers between each of these stages, especially because most of them involve dividing/multiplying by absolute numbers like 30seconds or 1000mg/g

All help is appreciated,
Alex

 

[mfb]

If you divide or multiply by constants the relative uncertainty stays the same. For evaporation rates within 30 seconds Gaussian error propagation will work.
For the average, this doesn't work, as your measurements are correlated: If a measurement (apart from the first and last one) is off, it will increase one rate and decrease another. It won't influence the average at all.

You can calculate the average and its uncertainty just from the first and last measurement, similar to the 30s values. You'll get a better estimate if you make a trend line through all your data, however.

 

[Dale]

what I am actually looking for which is a rate. I.e by finding the difference between each concurrent measurement, dividing it by 30seconds, then adding up each of the individual rates in g/s and calculating an average rate in mg/min.

A better approach would be to do a least squares fit to a regression line and obtain the slope. Most commercial packages will give you a standard error or a confidence interval for the slope.

There are ways to calculate what you suggest using the propagation of errors formula, but I would not recommend that approach.

 

[WWGD]

Doesn't the amount that evaporates at stage $t_0$ also depend on the total amount of water present at $t_0$?