Use the oversamplling followed by the "decimation method" to increase the ADC resolution and not normal averaging
I wouldn't take that application note too seriously &mdash; it contains many errors, both conceptual1 and typographical.

Adding up a bunch of samples and then scaling the sum by some factor, no matter what you call it, IS averaging. It's also filtering. It is, in fact, just one special case of a finite impulse response (FIR) filter, in which every sample gets its own scale factor and then they get added together to create the result.


  So, the question is, why do we need to use decimation method instead of the normal averaging after the oversampling to increase the ADC resolution?


It's all the same thing in the end.


  It says above "Right shifting a binary number once is equal to dividing the binary number by a factor of 2", but what if we don't use a binary number, how do we use the decimation method in this case?


Just use ordinary division if the divisor isn't a power of 2.



1 For example, "white" noise is NOT equivalent to "gaussian" noise, although many natural noise sources are both gaussian AND white.