Percentile function

Use the Minitab calculator to calculate the sample percentile for a specified probability and set of numbers. Percentiles divide the data set into parts. Usually, the nth percentile has n% of the observations below it, and (100-n)% of observations above it.

To use this function, choose Calc > Calculator.

For example, in the following graph, 25% of the total data values lie below the 25th percentile (red region), while 75% lie above the 25th percentile (white region).

Syntax

PERCENTILE(number,probability)

Calculates the sample percentile, for a specified probability and number (the column containing the sample data). Missing values are ignored. The probability must be between 0 and 1, inclusive, and indicates the percentile. For example, to determine the 1st quartile (25th percentile) of a column of data, enter the column number and the probability 0.25.

Example

Column	Calculator expression	Result
C1 contains 2, 3, 5, and 7	PERCENTILE (C1,0.25)	2.25

Formula

Minitab's calculator uses the empirical percentile function for the PERCENTILE function.

Notation

Term	Description
p	the percentage of data less than or equal to the desired percentile, divided by 100
X_y	the y^th row of the data when the data are sorted from least to greatest
y	the truncated value of w
w	p(N+1)
N	the number of rows with nonmissing data
z	w-y