# Percentile Calculator

   

An online calculator that calculates the data value corresponding to a given percentile and a second calculator calculates the percentile given a data value.

## Percentiles

The $n^{th}$ percentile of a set of data values is the value $V$ for which $n\%$ of the data values in the set are less than $V$. If $N$ is the number of data values, the position of the $n^{th}$ percentile is given by $\dfrac{N \times n}{100}$
Example 1
Find the $50^{th}$ and the $80^{th}$ percentiles of the data set given by:

52, 22, 30, 7, 12, 20, 21, 33, 45, 34, 9

Solution to Example 1
We first order the data set given above.

7, 9, 12, 20, 21, 22, 30, 33, 34, 45, 52

There are $11$ data values in the given set, hence $N = 11$.
The $50^{th}$ percentile is given by the position
$\dfrac{11 \times 50}{100} = 5.5$
Round to the nearest integer: 6
$22$ is the value in the ordered data set that is at the $6^{th}$ position. Hence the $50^{th}$ percentile of the given data set is 22.
The $80^{th}$ percentile is given by the position
$\dfrac{11 \times 80}{100} = 8.8$
Round 8.8 to the nearest lower integer 9.
34 is the value in the ordered data set that is at the position 9. Hence the $80^{th}$ percentile of the given data set is 34.

## 1 - Find the Data Value Corresponding to a Given Percentile Calculator

The data values must be separated by commas.

Data Set =
$^{th}$ percentile

Decimal Places =

## 2 - Find the Percentile Corresponding to a Given Value Calculator

The data values must be separated by commas.

Data Set =
Value =