How do we interpret the meaning of a percentile?
What I have learned from books is as follows: "If a score is the 40th percentile, this means that it is larger than 40% of the distribution, while the other 60% of scores are greater than or equal to the score."
My question is when that specific score equals to the previous score, shouldn't we say 40% of the distribution is "less or equal" to that score, instead of "less than" that score?
For example, say there are 500 students, and they are scored from 0 to 100. Say student A gets a score 80 and he is in 85th percentile, which traditionally means 85 percent student is less than his score and 15% is greater or equal to his score. In a specific case let 250 higher scorer students get all equal to a score of 80. Then student A is not higher than 85%. Or his score is not higher than the other student who also get 80. Is he?