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 =
Output
2 - Find the Percentile Corresponding to a Given Value Calculator
