A commenter named “Ray” writes in the comment section:

…I’d like to ask you if you can estimate the IQ of a cousin of me based on his intellectual milestones:
-Prior to his 1st birthday he spoke very well and he was very inquisitive
-At age 3 he learned to read and write on his own (my aunt taught him the alphabet, but she never taught him to read per se).
-At age 6 he was reading a college textbook on ondontology and he grasped a great deal of it, though he got bored afterwards-
-At age 6 he used to read textbooks on mathematics (prealgebra), social studies, Spanish Literature and 6th grade physics, chemistry and biology
-At age 12 he began reading Marx’s “Das Kapital” and became obsesed with economics and political philosophy afterwards

He’s currently 17, an avid reader and very well-versed in philosophy, economics and biology (genetics).
Based on this what would you think his IQ is? It’s clear that he has an astounding verbal IQ, though he is depressed because there are better students in math than him.
I hope you answer 🙂

I’ll focus on the three least ambiguous data points.

Research suggests that  at first toddlers “will be able to mutter only about four to six words, but at around 18 months, a real spurt in vocabulary will take place, and your Chatty Cathy’s list of go-to words will increase to about 50.”

It sounds like your cousin had acquired the speaking skills of a 1.5-year-old by age 0.9 or so, which would imply he was functioning at 167% of his chronological age and thus a ratio IQ of 167 (1.5/0.9 = 1.67)

Meanwhile reading and writing are not typically acquired until age six, so having achieved this at three implies he was functioning at 200% of his chronological age and thus a 200 ratio IQ (6/3 = 2.00)

Lastly, doing grade six (age 11) physics at age six implies a ratio IQ of 183 (11/6 = 1.83) though doing physics of any kind seems way beyond even 11-year-olds.

Averaging all three ratio IQs together (unlike deviation IQs, ratio IQs can be averaged) gives a ratio IQ of 183.

However ratio IQs are only normally distributed from IQ 50 to 150 (though with a slightly inflated mean and SD).

 

Above 150 there is an excess of scores, perhaps because the variance is greater at some ages than others and this becomes noticeable at extremes or perhaps because the linear relationship between age and cognitive development is limited to a narrow range, causing the ratio to become meaningless beyond these limits.

Modern IQ tests get around this problem by forcing scores to fit the bell curve.  So since it’s known that only one in 72,000 to 109,000 have ratio IQs in the 180s we can locate the normalized IQ (sigma 15) that fits this rarity, and we end up with an IQ of 164.

Of course this would only reflect your cousin’s early childhood IQ.  Given only about a 0.62 correlation between early childhood IQ and late adolescent IQ,  the typical IQ 164 child regresses into an IQ 140 young adult ((164 – 100)(0.62)) + 100 = 140 with 95% of cases ranging from 117 to 163.

However by age 10, IQ begins to solidify, and the fact that your cousin was enjoying Marx by age 12 implies his (verbal) IQ had remained above 140 (top 0.5%).  Charles Murray notes that just under 10% of even young adults can score high enough on the verbal SAT to likely understand traditional college reading and I’ve found that the top 10% of young adult verbal skill equates to the top 0.5% of age 12 verbal skill.  And Marx might be a lot harder than even traditional college material so I might be dramatically underestimating your cuz.

But even 140 (white norms) is incredibly high.  It might not sound that impressive when you hear that Harvard’s average SAT score equated to an IQ of 143, but just as your cousin’s childhood IQ of 164 might have regressed to an adult IQ of 140, Harvard’s SAT derived IQ of 143 likely regresses to an IQ in the 120s on official IQ tests.

So even 140 is enough to tower at even the most elite universities on the planet (at least in the non-STEM departments).

140 is to IQ as 6’6″ is to height: Head and shoulders above the competition.