QSoas quiz #1 : averaging spectra

Here is the first QSoas quiz ! I recently measured several identical spectra in a row to evaluate the noise of the setup, and so I wanted to average all the spectra and also determine the standard deviation in the absorbances. Averaging the spectra can simply be done taking advantage of the average command:

QSoas> load Spectrum*.dat /flags=spectra
QSoas> average flagged:spectra

However, average does not provide means to make standard deviations, it just takes the average of all but the X column. I wanted to add this feature, but I realized there are already at least two distinct ways to do that...

Quiz

Your task is to determine the average and standard deviations of the three spectra located there, (Spectrum-1.dat, Spectrum-2.dat and Spectrum-3.dat). There are at least two ways:

• One that relies simply on average and on apply-formula, and which requires that you remember how to compute standard deviations.
• One that is a little more involved, that requires more data manipulation (take a look at contract for instance) and relies on the fact that you can use statistics in apply-formula (and in particular you can use y_stddev to refer to the standard deviation of \(y\)), but which does not require you to know exactly how to compute standard deviations.

To help you, I've added the result in Average.dat. The figure below shows a zoom on the data superimposed to the average (bonus points to find how to display this light red area that corresponds to the standard deviation !).

I will post the answer later. In the meantime, feel free to post your own solutions or attempts, hacks, and so on !

About QSoas

QSoas is a powerful open source data analysis program that focuses on flexibility and powerful fitting capacities. It is released under the GNU General Public License. It is described in Fourmond, Anal. Chem., 2016, 88 (10), pp 5050–5052. Current version is 2.2. You can download its source code or buy precompiled versions for MacOS and Windows there.