Each of the numbers that divide a set of observations into 100 parts with equal frequencies.

Each of these parts represents 1/100 of the sample of the population observed.

The percentile rank corresponds to the proportion of the values of a distribution that is less than or equal to a determined value.

### Formula

To calculate the percentile rank *R*_{100}(*X*) of an element *X* of a statistical distribution containing *n* elements, you must first arrange the values in the distribution in order, then find the number *Di* of the elements less than *X* and the number *De* of elements equal to *X*. Then, apply this formula:

\(R_{100}(X)=\dfrac{Di + 0.5De}{n}×100\)

### Examples

- If a student earned a grade of 84% on a math test and if this grade is greater than or equal to the grades earned by 75% of the students, this places the student in the 75th percentile of the group observed.
- Consider this distribution: 45, 80, 27, 32, 41, 49, 53, 77, 51, 41, 33, 55, 32, 77.

To calculate the percentile rank of the individual who got the grade of 41, determine the following values:*Di*= 4 and*De*= 2. Next, apply the formula:

\(R_{100}(X)=\dfrac{Di + 0.5De}{n}×100 = \dfrac{4 + 0.5 × 2}{14}×100 \)

Here, we get 35.714 285 … ≈ 35.71.

Round the number up to nearest integer, which is 36.

Therefore, the percentile rank of this individual*X*is: \(R_{100}(X)\) = 36.