Is there a way to define the concept of standard deviation for binary norms like Hamming norm?
For two words (in most general case - sequences of symbols from a given alphabet) of the same length, Hamming norm gives a number of different letters. If we have a series of words $A = \{ x_i \}$, $i = 1, ..., N$, and also a reference word $x_0$, we can measure Hamming distance $H_i$ between each word $x_i$ and reference word $x_0$.
How can we introduce a concept of average word $\langle x \rangle$ to then come to a definition of standard deviation which would characterise how individual words $x_i$ are scattered?