Re: Statistical Profile of an Average Joanna Newsom Fan
Posted: 22 Oct 2015, 13:35Dipping my toe into this rather rarified discussion, could I venture that the word "normal" simply implies - in everyday parlance - a correlation to 'the norm', and this latter term can be defined unemotively and statistically. Whilst I do have a (long ago) background in mathematics, I suggest that it's important that the thrust of the argument doesn't get lost in the slightly different ways in which the word "normal" is used in colloquial as opposed to technical language.
Therefore, whilst it could be argued that a statement such as "In Portugal, people aren't normally Protestant" (and setting aside the possible ambiguous interpretation that they may be abnormally Protestant) might be seen as implying some kind of disapproval (whether of Protestants, non-Protestants, or Portuguese people will probably be coloured by the tone and setting of the utterance), all it is really saying is that there exists a statistically verifiable demography of the Portuguese population, and that Protestantism is in the minority.
Where the variable lends itself to a sequence with an actual or implicit mapping onto a number line, such as a person's height, income, age, or number of children*, then we sometimes (though not always) see the familiar bell-curve of the Normal Distribution (though not always: it is easy to visualise, in my third example, that the curve will have a maximum at zero, and tail off into the distance in the positive segment, but - obviously - with a zero frequency for all negative numbers of children!) The definition of what is normal and what is not then reduces to an argument about how much 'tolerance' one is prepared to allow about the maximal value, beyond which a given reading might be ragarded as abnormal.
I might add that there is a category of variables which, although not intrinsically following an ordered number line, can be assigned points on a linear X-axis, or even on an XZ plane: Sexual orientation may be susceptible to the former (with 'profoundly straight' at one end, and 'profoundly homosexual' at the other), and ethnicity an example of the other, where a certain racial characteristic can be plotted against the point on the map from which it originated (I'm avoiding yet more complication by assuming the globe can be represented meaningfully on a plane: fortunately, there aren't very many inhabitants of the Polar regions to distort the argument in a north-south direction, but that argument doesn't hold quite as well in the east-west direction, where peoples trans-cend [couldn't resist] the traditional but arbitrary line that separates New Zealand from the Cook Islands). Neither of these approaches is without controversy, and it also makes light of possible blendings of variable (Where would one plot the child of a British sailor and his Hong Kong bride? And would it be meaningful to pinpoint someone of Afro-Caribbean origin in, say, Ghana, if his ancestors had lived in Jamaica for generations?)
However, not all variable are like that. Religion would be a good example (along with 'make of car driven', eye-colour, and many others): it would be a very artificial construct, if one tried to list these characteristics in some fort of order, and then plot a distribution on the foregoing basis that was meant to define what is normal and what is not. Nevertheless, that does not prevent us from identifying someobvious points of reference: Wikipedia tells me that four-fifths of Portugal's population identify as Catholics, and so it would not be misleading to say that 'a normal Portuguese person is Catholic'. Where a problem arise would arise is if we try to calculate this using some kind of formula, unless it is simply to split the population into two categories: Catholic and Non-Catholic. In other words, a system that tried to order or 'weight' someone's religion, even ignoring any perceived offence to groups allocated low or negative numbers, would be intensely problematical. Try is: suppose we say that Catholicism is allocated a number, 10 for example. Then perhaps Protestantism (in all its forms) might be allocated, say, 8. Other abrahamic religions could be given numbers close to 10: how about Judaism = 12, and Islam 14. It may just be possible to allocate numbers to, for example, certain quasi-Christian belief sets could be allocated slot 6. But then, where on earth would one put Buddhists, animists, followers of Norse gods, and other categories that are only loosely related to Christianity. And if one cannot place the characteristics in some sort of order, then it becomes impossible to plot a meaningful frequency diagram.
So to sum up, I would agree with Jordan~'s final statement that "Statistical norms are seldom salient outside of contexts with a peculiar concern for statistics", but that it might be enlightening to draw other conclusions of a non-statistical basis if the responses to "What is an average Joanna Newsom fan" demand them. If Mercedes-driving Scientologists were in the majority here, it would surely be worthy of note, even if it would be impossible to factor in the effect of an influx of Buddhists with Aston Martins to arrive at a new weighted average.