## Wednesday, October 7, 2020

### 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 !