An online calculator that calculates the data value corresponding to a given percentile and a second calculator calculates the percentile given a data value.
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 \[ \dfrac{N \times n}{100} \]
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
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.
The data values must be separated by commas.
Data Set =
\( ^{th} \) percentile
The data values must be separated by commas.
Data Set =
Value =