It seems to me too that this should also be correct. http://www.franceculture.fr/oeuvre-la-sante-par-quels-moyens-et-a-quels-prix-de-pierre-yves-geoffard'
La santé, par quels moyens et à quels prix ?
'Moyenne" is an adjective or noun that means "average". http://www.larousse.fr/dictionnaires/francais-anglais/moyenne/209588
I think English "mean"(average) and "middle", and French "moyen" are all derived from the Latin root "medianus" (?) that gave us "median". The several other definitions of mean in English and French seem to come from a Germanic root. Looks like two separate sources accidentally gave rise a similar word.
...how did I get sidetracked into thinking about all this? Back to the DL practice!
In English, it is roughly equivalent to saying, "How"? Eg:
A: I will fly to the moon. B: By what means?
Literally, "means" here is used to imply a device or method. So, the phrase is equivalent to, "by what device or method"?
So, "how" is a more vague question; "by what means" is more specifically focusing on the method by which this thing will be done.
Partly, yes. You got the "by" bit correct. You need to think of this example as similar to "by what method?" or "by what manner" .......or "how?"
Eg. By what means did he kill her? (How?) By what means will you be able to buy a new car? (How will you be able to buy a new car when I know you don't have any money?)
Route suggests a set of directions, such as when you're planning a trip.
I'm really just talking about his particular instace. I found the correlation between mean and average in the maths context a bit clarfying for myself and thought it might help someone else, considering there must be some... "etimologic" connection, they come from the same frame of mind.