About 50% of people are below average
This cracks me up because it is often said with such confidence, but it is just wrong.
If you have 10 people, 8 have an intelligence score of 1, 1 has a score of 5 and 1 has a score of 10. The average is 2.3 which means that 80% of the people are below average.
The median is the only thing that is going to guarantee 50%.
Technically, if everyone gets the full mark, no one will be in the bottom quartile.
I’m overthinking this.
If everyone gets the full mark, it’s not a random variable anymore, you would have a collapse of the probability distribution, that would tend to a Dirac delta function. In this case, the very definition of “quartiles” would fail. So, yeah, there would be no one there because it wouldn’t exist.
