# Percentile

## Percentile

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 R100(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.