IQ, College, Engineering, Law, And National Merit Scholarships

College

Students who are below a 22 on the ACT composite, a 1073 on the new SAT composite, a 1610 on the older SAT composite, are not in the top 35% of his high school class (in a high school that is representative of the general population), or have below a B+ GPA, have a significantly impaired, low chance of graduating with a four year degree. 

This cutoff is not very sensitive to the selectivity or to the type of institution attended.

The threshold for any ordinary college program corresponds to an IQ of about 110 on a 15-point standard deviation scale or 111 on a 16-point standard deviation scale which is about the 75th percentile of the general population (a higher percentage because the general population includes high school dropouts who aren't included in SAT and ACT percentiles).

But a strong work ethic and grit can make it possible for you to graduate despite a lower IQ in many majors.  

Certain programs (e.g. some STEM programs such as math, physics and engineering), however, have a higher effective minimum threshold for a student to have a reasonable chance of graduating. Basically 0% of people who earn such a degree have an IQ of under 111 (and the threshold to have a better than 50-50 likelihood of graduating is an IQ of 119). Unlike some undergrad majors, engineering has a strong threshold effect.

Under 15-point standard deviation WAIS IQ scaling standard, an IQ of 100 is average for the population as a whole, an IQ of 105 is average for a high school graduate, and an IQ of 115 is average for a college graduate. So, an effective cutoff IQ of about 110 for a reasonable likelihood of graduating from college, fits with the concept that one must be discernibly better than average high school student to be likely to graduate from a college or university with a four year degree.

The Bar Exam

Maximal test prep can increase an LSAT score by about 3 point in the 120-180 range of the test. The maximum impact on other standardized tests scores is similar (but there is more room to improve in math than verbal on the SAT).

An IQ of 100 is roughly an LSAT score of 133, and almost no one who gets below 145 on the LSAT has any realistic chance of passing the bar exam. The bar exam is highly correlated with IQ test results. It takes an IQ of about 117 to pass the bar exam eventually after multiple tries, and the average IQ of a lawyer who passes the bar exam is about 133. (Medical school is much more selective.)

The patent bar is even harder to pass with a low IQ because to be a lawyer admitted to the bar and be a patent lawyer at the same time, you need an engineering BA (there are exceptions but similarly rigorous ones). 

National Merit Scholarships

About 2300 National Merit Scholarships were awarded in the year 2010. It turns out that just 10 elite universities accounted for well over half of these awardees. 

Number of NMS in entering class / size of entering class.

Caltech 42 / 200

Harvard 266 / 1600

Yale 234 / 1300

Princeton 196 / 1300

Stanford 110 / 1600

MIT 110 / 1000

Brown 91 / 1500

Duke 105 / 1600

Penn 125 / 2000

Berkeley 91 / 6000

Total 1270