var (Statistics Toolbox)

var	Examples See Also

Variance of a sample.

Syntax

y = var(X)
y = var(X,1)
y = var(X,w)

Description

var(X) computes the variance of the data in X. For vectors, var(x) is the variance of the elements in x. For matrices, var(X) is a row vector containing the variance of each column of X.

var(x) normalizes by n-1 where n is the sequence length. For normally distributed data, this makes var(x) the minimum variance unbiased estimator MVUE of

²(the second parameter) .

var(x,1) normalizes by n and yields the second moment of the sample data about its mean (moment of inertia).

var(X,w) computes the variance using the vector of weights, w. The number of elements in w must equal the number of rows in the matrix, X. For vector x, w and x must match in length. Each element of w must be positive.

var supports both common definitions of variance. Let SS be the sum of
the squared deviations of the elements of a vector x, from their mean. Then, var(x) = SS/(n-1) the MVUE, and var(x,1) = SS/n the maximum likelihood estimator (MLE) of

².

Examples

x = [-1 1];
w = [1 3];
v1 = var(x)

v1 =

     2

v2 = var(x,1)

v2 =

     1

v3 = var(x,w)

v3 =

    0.7500