Question

11 students in the AP Calculus class received the following scores on their term final, who ranks in the 82nd percentile for the class?

tami-75%
eric-83%
sarah-97%
omar-95%
shakira-88%
lucy -65%
jacob-70%
jose-83%
david-67%
hassan - 91%
kim-72%

Answer 1

Omar ranks at the 82nd percentile.

Explanation:

For someone to rank at the xth percentile, it means that x percent of students score below him or her. So, for someone to rank at the 82nd percentile, it means 82% of students must score below him or her.

If you rank the students in order of highest to lowest, Sarah is first, then Omar, then Hassan, then the rest. Since he performed second best, Omar performed better than 82% of students (or 9 out of 11 students). Thus Omar ranks at the 82nd percentile.

For what it's worth, Sarah ranks at the 91st percentile, even though no one scored higher than her. This is because the total sample size itself is quite small (only 11 students).