Let's start with university. In the UK, along with many industrialised societies, something like 40% of the cohort go to university. This sets the entrance level at the 60th percentile. Looking up the value of 0.1 (corresponds to 0.6 = 0.5 + 0.1) in a normal distribution table tells us that this occurs at 0.25 standard deviations to the right of the mean. Since IQ is normed at mean = 100, standard deviation = 15, the minimum IQ to get into university these days is about 104.
Obviously if this is your IQ you're going to be doing media studies or drama, not economics, mathematics or physics. It's a floor.
Now we turn to another useful chart, this time from Steve Hsu via Lubos Motl. I reproduce part of Lubos' rather satirical post below. Steve Hsu's original data was GRE (Graduate Record Examinations) scores, which he then translated into IQ scores. The GRE are taken by most American university graduates seeking to do post-graduate study to PhD level. Anyway, here's Lubos:
"Steve Hsu has found a very interesting table with the average GRE scores computed for various concentrations. He has also defined a linear map translating the average V-Q-A scores into a more familiar IQ scale. This convention looks natural to me and I will follow his scale although it is not guaranteed that it is equally calibrated as other IQ measurements.Since these are graduate entry levels, they're creaming off the top end of undergraduates. So it's kind of an 'undergraduate good 2:1' floor we're seeing here. Oh, and scary & surprising about US doctors, don't you think? In the UK, the average IQ of medical students is reckoned to be 125 (page 61).
"Disclaimer: these cold numbers expressing typical IQ for different occupations must be interpreted very carefully. They don't necessarily imply anything. The outcome depends on the character of the question, discrimination, etc. Despite different numbers, all of us are equal. Blah blah blah. And so on.
"The results are: [A PhD student's typical IQ for this subject]
128.5 Computer Science
127.5 Chemical engineering
127.0 Material science
126.0 Electrical engineering
125.5 Mechanical engineering
123.0 Earth sciences
122.0 Industrial engineering
122.0 Civil engineering
119.8 Political science
118.0 Art history
106.0 Public administration"
At the very top-end, Steve Hsu has observed:
"I doubt that the average among eminent scientists (averaging over all fields) is 160; probably a bit lower like 145."Finally I draw your attention to "Smart Fraction" Theory, which examines the notion that to run a modern, complex, industrialised society requires a mass of people with (verbal) IQs greater than around 106. Our best societies today have a smart fraction just under 50% (see graph at the bottom of the linked article).