In Idiocracy, they show an average IQ chart that is declining over the next few centuries. Now, anyone who's studied IQ knows that's nonsense. The average IQ of a population is by definition 100. So, is this merely an instance of inadequate research by the writers, or is there an actual meaning to that chart?
It's a comedy.
Don't think too hard about a future where populations basically use a Gatorade-equivalent to water plants. It's merely a representation that people are stupid.
Even following internal logic, they'd be stupid enough to forget to (or even how to) calculate accurate median or general averages.
That's one of the key differences between a scientific paper (where exactly correct use of scientific terms and concepts are important) and a work of art (which has no such restrictions).
The main theme of the movie is "What would happen if humans were gradually becoming less intelligent?" (the use of 'what...if' being a common meme in science fiction). How is this concept going to be conveyed to the audience? A graph shows a decline in some measure of intelligence. Is it scientifically accurate or correct? Perhaps not. Is it effective in conveying an important concept to the audience? Yes.
On the other hand, one could argue that the population over which the median is being calculated is every person who every lived and not just every person who is alive now. In that case, the average IQ of those who are alive now could be gradually declining.
Actually, you're thinking of IQ Tests representing the median raw score as 100 as an average like in the Wechsler Intelligence Scales.
As stated in the IQ Classification Wiki:
The Wechsler intelligence scales were originally developed from earlier intelligence scales by David Wechsler. The first Wechsler test published was the Wechsler-Bellevue Scale in 1939. The Wechsler IQ tests for children and for adults are the most frequently used individual IQ tests in the English-speaking world and in their translated versions are perhaps the most widely used IQ tests worldwide. The Wechsler tests have long been regarded as the "gold standard" in IQ testing. The Wechsler Adult Intelligence Scale—Fourth Edition (WAIS–IV) was published in 2008 by Psychological Corporation. The Wechsler Intelligence Scale for Children—Fourth Edition (WISC–IV) was published in 2003 by Psychological Corporation, and the Wechsler Preschool and Primary Scale of Intelligence—Fourth Edition (WPPSI–IV) was published in 2012 by Psychological Corporation. Like all current IQ tests, the Wechsler tests report a "deviation IQ" as the standard score for the full-scale IQ, with the norming sample median raw score defined as IQ 100 and a score one standard deviation higher defined as IQ 115 (and one deviation lower defined as IQ 85).
When they say that the average IQ of the population declined they are representing that the median score of the entire population was declining.
There is a website that shows the countries with the lowest average IQ of a population here
Equatorial Guinea's population has an average IQ of 59, while Ethopia has one of 63, which is well below 100.
Here's a real life chart too from
As you can see, in a 100 year period the world's average IQ will have dropped from 92 to 86, a change of 6%. That is pretty darn significant. And all because of differential population growth.
As the original question says, IQ scores are by definition normalized to have mean 100. Interestingly, if you don't renormalize but grade current students by old standards, IQ scores appear to be rising. This is known as the Flynn effect.