The question asked:
1,000 students took an English proficiency exam that awarded only whole number grades. The scores are distributed as follows:
100 students scored between 0 and 20, inclusive.
200 students scored between 21 and 40, inclusive.
300 students scored between 41 and 60, inclusive.
300 students scored between 61 and 80, inclusive.
100 students scored between 81 and 100, inclusive.
What is the top possible score of a student who falls within the 60th percentile?
The answer is 60, but I think it should be 80.
A percentile divides an ordered list into 100 equal groups. So if I were to do that:
The 1st to 10th ranked students belongs to the 0th percentile
The 11th to 20th ranked students belong to the 1st percentile
The 21st to 30th ranked students belong to the 2nd percentile
.
.
The 581st to 590th ranked students belong to the 58th percentile
The 591st to 600th ranked students belong to the 59th percentile
The 601st to 610th ranked students belong to the 60th percentile
Students that are ranked between 601st and 610th correspond to the group that scored between 61 and 80. This group also corresponds to students that are ranked between 601st and 900th. Hence, the top possible score of a student who falls within the 60th percentile is 80.
Did I make a mistake somewhere?