# Points from detectors: when to integrate, sum or average?

I'm reading data from detectors like Mass Spectrometers, DAD, etc. One measurement from these detectors gives a spectrum, so there are many data points in some range e.g. from 200 to 1000 m/z or from 200 to 400 nm. Users want to get the intensity let's say at 400m/z. But detectors measure things with a finite resolution, so we should really give them 400 ± 0.2 for instance. But now what do we do with the points in this range?

I looked into other software and they seem to be doing this differently between themselves and between detectors:

1. Some would simply sum up the points in the range
2. Others would integrate the area between 399.8 and 400.2
3. And there are those that sum and divide by the number of points

What's the ideology here - when should we do what?

Also:

1. Points are not always spaced regularly
2. Another difference between sum and integration: when doing sum point 400.3 won't be included. In case of areas - the space between let's say 400.0 and 400.2 will still be integrated - so 400.3 has an effect on the result.
• I think all methods will yield the same results except for the scale. An integration is the sum of a sequence of points if they are regularly sampled. An average, is dividing a sum by the number of points.
– Ben
Commented Nov 23, 2021 at 17:16
• @Ben, well, the points aren't necessarily regularly spaced :) Commented Nov 23, 2021 at 17:28
– Ben
Commented Nov 23, 2021 at 17:28
• @Ben, done. And added yet another difference. Commented Nov 23, 2021 at 17:30

Ideally you would compute and report the standard deviation for your measurement result, and state that your $$\pm$$ criteria is a one sigma standard deviation.
Examples of this are doing "Absolute Average Deviation" instead of standard deviation which for white noise is related by $$\sqrt{2/\pi}$$. Another example is doing post detection averaging (such as on a spectrum analyzer) and then if the results are averaged in dB or magnitude quantity. This is detailed in this great app-note 1303 by the former HP now Agilent where we see the results will be in error of the actual standard deviation by -2.51 dB when averaging log-detected signals and -1.05 dB in averaging detected signals (with the point that the average of the squares is not the same as the square of the averages).