From my point of view, INTJ's and INFJ's are the rarest, but tend to be more and more common the closer you get to a university.
My best friend is an ESFP, albeit the smartest ESFP i know.
And my girlfriend is an INFJ. Who happens to be my best friends ex.
I also just saw a girl I had a huge crush on for a good while last year, walk out of my best friends bedroom and to the bathroom. As we share an apartment together.
So, eh!...
My life got messy as soon as I saw value in friends and of being social.
I've had a lot of acquaintances throughout my life so far, and can only pin a handful of people as either INFJ or INTJ.
Type testing seems to be biased in respect to intelligence, that is, an intelligent person is more likely to score N, just because they are more intelligent and that affects behavior in a similar seeming way as type does. But an intelligent ISTJ that score INTJ and is identified and identifies with INTJ will more easily tell the difference if compared in person to a equally or more intelligent INTJ. So one could perhaps even argue that the S/N dichotomy is entirely artificial and superfluous and act only as an identifier for whether you are generally more intelligent then your peers.
My ESFP best-friend has an IQ of around 122, and I have a measured IQ of 135+. Don't know what the IQ of my INFJ girlfriend is, but would be surprised if it isn't around 130. My friend at least thinks that the both of us are the two most intelligent people he knows.
And he tested originally ENTP, then leaned on ENFP. And now identifies with and is comfortable with ESFP, but is perplexed about his peers.
And then back to rarity,
http://libertycorner.blogspot.com/2004/03/iq-and-personality.html
Whether that is due to intelligent people testing more often as N, or if N people are just more intelligent on average, is a bit besides the point.
Because with IQ there is a statistical distribution and a bell curve, so if there is something to MBTI, it will also have such a distribution.
And INxJ having such strong representation there, is, if not anything else; a strong indication of rarity! But that of course has to be properly tested...
Would anyone be interested in funding some research in order to answer that question?
Oh, and I know a lot about IQ, because it is one of those things I explored to try and explain and understand my self; how and why i dysfunction!
My numbers are from a neuropsychological examination that says I'm neither autistic, nor have behavioral disorders, but are in fact just 'gifted'.
I value creativity and insight much higher then IQ, as creativity is essential. Understanding *everything* fast and effortlessly is not.
IQ is helpful, but not a necessity. As nothing worthwhile comes effortlessly, that remains true no matter how smart you are. You just affect the level of complexity you are comfortable at. And as both in science and art, something that 'feels' true is never complex. The complexity is in arriving at that simplification or more succinctly, a rule, the more elegant thus stronger it is.
And incoming cliche: I study philosophy and is regarded in that, as someone that is a free thinker and philosophically gifted -- someone having that certain way of seeing.
But now I hear kissing noises from the next room, they're probably just fucking with my head, but one never knows.
Now I just miss my girlfriend, and have said what I wanted to.