Rank, Percentile Rank

Rank, Percentile Rank

How to find the rank and the percentile rank from the given data: formula, examples, and their solutions.

Example 1

The following data show test scores for 20 students: 81, 56, 74, 52, 78, 81, 77, 91, 85, 60, 75, 69, 97, 84, 70, 67, 80, 74, 74, 88. Find the percentile rank of 81 points.

(Rank) = (number of smaller values) + 0.5⋅(number of the same values)

(number of smaller values) = 13
(number of the same values) = 2

(Rank) = 13 + 0.5⋅2 = 14

(Percentile Rank) = (Rank)/(number of the data) × 100

(Rank) = 14
(number of the data) = 20

(Percentile Rank) = 14/20 × 100 = 70 th

Example 2

The following data show test scores for 20 students: 81, 56, 74, 52, 78, 81, 77, 91, 85, 60, 75, 69, 97, 84, 70, 67, 80, 74, 74, 88. Find the percentile rank of 74 points.

(Rank) = (number of smaller values) + 0.5⋅(number of the same values)

(number of smaller values) = 6
(number of the same values) = 3

(Rank) = 6 + 0.5⋅3 = 7.5

(Percentile Rank) = (Rank)/(number of the data) × 100

(Rank) = 7.5
(number of the data) = 20

(Percentile Rank) = 7.5/20 × 100 = 37.5.

The percentile rank has to be rounded
to the nearest ones.
So 37.5 → 38th.