# Percentile Calculator

You can use this percentile calculator to efficiently determine the p-th percentile for a set of numbers.

How to use the Percentile Calculator:

1. Input the numbers in the set separated by a comma (e.g., 1,9,18,12), space (e.g., 1 9 18 12), or line break.
2. Enter the percentile value you wish to determine.
3. Click on the "Calculate" button to generate the results.
Pth Percentile Calculator

Results
Solution:

## Definition of Percentile

The pth percentile is the value in a set of data at which it can be split into two parts. The lower part contains p percent of the data, and the upper part consists of the remaining data; i.e., 100-p (the total data equates to 100%).

## Calculating the pth Percentile

You can use the following process to manually determine the pth percentile of a set of data.

1) Arrange the data such that the entries span from the smallest to the largest values (ascending order).

2) Calculate an index i (the position of the pth percentile) as follows:

i = (p / 100) * n

Where: p is the percentile and n is the number of values that appear in the data.

If i is not an integer, round it up. The next integer greater than i represents the position of the pth percentile. If i is an integer, the pth percentile is the average of the values in positions i and i + 1.

## Examples

Let's say we want to determine the 80th percentile for the following values: 10, 55, 50, 80, 85, 90, 20, 40, 55, 65, 30, 25.

1) Arrange the values from lowest to highest: 10, 20, 25, 30, 40, 50, 55, 55, 65, 80, 85, 90.

2) Calculate index i (the position of the pth percentile):

i = (p / 100) * n = 80 / 100 * 12 = 9.6

3) In this case, i is not an integer. As such, you should round up. The point of the 80th percentile is the next integer above 9.6, which is the 10th position.

4) The 80th percentile is the data value that appears in the 10th position in the list of values: 80.

Let's look at a second example. This time, we want to calculate the 50th percentile for the set of data.

1) Having arranged the values in ascending order, we have: 10, 55, 50, 80, 85, 90, 20, 40, 55, 65, 30, 25.

2) Calculate index i (the position of the pth percentile):

i = (p / 100) * n = 50 / 100 * 12 = 6

3) In this case, i is an integer. As such, the 50th percentile is the average of the values that appear in the 6th and 7th positions in the set of ordered data: 50 and 55 respectively. Therefore, the 50th percentile of this data set is (50 + 55) / 2 = 52.5.

You may also be interested in our Interquartile Range Calculator