this post was submitted on 21 Sep 2023
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Technically, if everyone gets the full mark, no one will be in the bottom quartile.
Also, everyone would be in the bottom quartile. The definitions fall apart when you collapse the probability function.
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.
Well it can be a RV. Just one that is uniformly distributed over the set {x}, where x is the full mark score. Or however you want to put it.
It is a rather useless and uninteresting RV but nontheless is is one....