This is my definition:

What is “normal” can only be defined by a person for his or herself. Hence we are all normal to ourselves and everyone else by default is weird. Normality in other people is only representative of when a person demonstrates enough of the same traits that you consider normal for yourself.

You can equally define normality against a social or community based construct, however, amongst any group of people there will be outliers that do not conform and thus normality is more of a definition by dictatorship. Whoever controls the society controls what is defined as normal.