Edit: This post is quite long but does anyone else have the same confusion?

I am quite confused with the way percentiles and quartiles are **expressed**.

Typically, as per my understanding, if we say that a value is **AT** the 75th percentile, that will mean that that value is equal to P75 (as per the definition in ETS GRE Math Review). In contrast, if we say that candidate X’s test score is **IN** the 75th percentile, we usually mean that he scored more than 75 percent of the people who took the test. In other words, if I am interpreting this correctly, his score lies somewhere between P75 and P76. And, as per my understanding, we can think about Quartiles in the same way.

However, here is what Math Review says. Please read the highlighted portion only. Rest is only for reference.

Which means 4 lies between

**L and Q1**, right? But according to my understanding that I said above, 4 being

**IN**the first quartile (or 25th percentile) should mean that 4 should lie somewhere between Q1 and Q2 (25 percent of values being lesser)

What am I getting wrong here?