Percentile Rank — Definition, Formula & Examples

Percentile rank is the percentage of values in a data set that are equal to or less than a particular value. If your test score has a percentile rank of 80, that means you scored equal to or higher than 80% of the test-takers.

The percentile rank of a score $x$ in a data set is the proportion of observations with values less than or equal to $x$ , expressed as a percentage. It maps each raw score to a value between 0 and 100, indicating that score's relative standing within the distribution.

Key Formula

\text{Percentile Rank} = \frac{L + 0.5S}{N} \times 100

Where:

$L$ = Number of values in the data set that are less than the given score
$S$ = Number of values in the data set that are equal to the given score
$N$ = Total number of values in the data set

Worked Example

Problem: A class of 20 students took a quiz. One student scored 74, and 13 students scored below 74 while 2 students (including this one) scored exactly 74. Find the percentile rank of 74.

Identify values: Count the scores below 74 and the scores equal to 74.

L = 13, \quad S = 2, \quad N = 20

Apply the formula: Substitute into the percentile rank formula.

\text{Percentile Rank} = \frac{13 + 0.5(2)}{20} \times 100 = \frac{14}{20} \times 100 = 70

Answer: A score of 74 has a percentile rank of 70, meaning this student performed as well as or better than 70% of the class.

Why It Matters

Standardized tests like the SAT, ACT, and state assessments report percentile ranks so you can compare your performance against all other test-takers. In AP Statistics, understanding percentile rank is essential for interpreting cumulative relative frequency graphs and solving problems about distributional position.

Common Mistakes

Mistake: Confusing percentile rank with percentile. Students think "80th percentile" and "percentile rank of 80" are different things.

Correction: They describe the same idea from opposite directions. The 80th percentile is the score at which the percentile rank equals 80. Percentile rank starts with a score and finds the percentage; percentile starts with a percentage and finds the score.