`quantile`

Quantiles of a sample.

Category: Data Import and Analysis > Descriptive Statistics

Syntax

Y = quantile(X, p)

Quantiles p (from 0 to 1) of the vector X, or of each column of a matrix.

Y = quantile(X, p, dim)

Along dimension dim.

Description

The quantile for probability p is the value below which a fraction p of the data lie. quantile(X, 0.5) is the median, and p = 0.25, 0.75 give the quartiles. Between observations the function interpolates linearly, treating the sorted values as the midpoints of equal probability bins; below the first and above the last midpoint it returns the minimum and maximum.

Quantiles describe the distribution without assuming a shape, and are resistant to outliers.

Input arguments

X: Numeric vector or matrix.
p: Cumulative probabilities between 0 and 1, scalar or vector.
dim: Dimension to operate along.

Output arguments

Y: The requested quantiles.

Example

Quartiles of a matrix

x = [3 1 4 1 5 9 2 6 5 3];
quantile(x, [0.25 0.5 0.75])
A = [1 5; 3 2; 4 9];
quantile(A, 0.5, 2)

Output

ans = 1×3

    2.0000    3.5000    5.0000
ans = 3×1

    3.0000
    2.5000
    6.5000

quantile