TL;DR: You can average them to get a single number, but just know that this will throw away other useful information.
This question has been asked before a couple times, so I’ll reference some previous posts:
The Muse SDK doesn’t provide a single overall measure for each frequency band. It provides relative and absolute measures of band power from each electrode site. I can’t say what exactly the studies you’ve read have done to calculate a single monolithic “Alpha” value. Perhaps they averaged the Alpha power of some set of electrodes over a certain period of time. They almost certainly captured data from several different electrode sites and obtained measurements of Alpha power for each. How they consolidated them, I can’t say for sure. It’s hard to get specific without reading the actual studies/papers, which usually state their methods.
It makes sense to have separate indications of band power for each electrode, as different sites will tend to produce different amounts of activity. That way you can combine information from each channel however you like, to obtain a fuller picture of what is going on and tailor the output to your application. If you average all the electrodes together, you’ll be throwing away spatial information as well as reducing the influence of sites that tend to produce a certain type of activity.
If what you’re really interested in is single indicators of different types of activity, i.e. black-box style outputs, we are gradually adding these to the SDK. You can give our experimental “concentration” and “mellow” measurements a try, for instance.
Averaging the band powers across channels will throw away spatial information, for one thing.
When you average the signals from all the electrodes, you may end up amplifying whatever information is common to all of them, which is the common-mode noise, something you want to ignore. Since some electrode locations exhibit more activity in certain bands than others, averaging will reduce their individual influence. For example, the ear electrodes tend to pick up more alpha than the forehead electrodes, so averaging them all together would just downplay the presence of alpha overall, and increase the presence of certain types of noise.
In fact, an average of all electrodes or some subset of electrodes is commonly used as a reference in standard EEG methodology. In other words, an average of a bunch of electrodes is considered in the literature to be representative of the common-mode noise.