I have a time series of data points read from an instrument, I also get an estimate of the error ($\sigma$) for each of these readings.
e.g.
$10.12 \pm 0.05$
$10.09 \pm 0.02$
$10.20 \pm 0.12$
etc.
To reduce the noise inherent in the data I'm binning (averaging) them with respect to time intervals, all fine and simple even with my basic maths knowledge. But what is the correct way of combining the errors readings?
Best Answer
I will show two calcultions.
Example: w = (4.52 ± 0.02) cm, x = ( 2.0 ± 0.2) cm, y = (3.0 ± 0.6) cm. Find z = x + y - w and its uncertainty.
z = x + y - w = 2.0 + 3.0 - 4.5 = 0.5 cm
METHOD 1
Delta z = Delta x + Delta y + Delta w = 0.2 + 0.6 + 0.02 = 0.82 rounding to 0.8 cm
So z = (0.5 ± 0.8) cm
METHOD 2
Solution with standard deviations
Delta z = SQRT((Delta x)^2 + (Delta y)^2 + (Delta w)^2)
Delta z = 0.633 cm
z = (0.5 ± 0.6) cm
Notice that we round the uncertainty to one significant figure and round the answer to match.
Now you can apply this to your measurements.