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Variance
V = var(X)
V = var(X,1)
V = var(X,w)
V = var(X,w,dim)
V = var(X) returns the variance of X for vectors. For matrices, var(X)is a row vector containing the variance of each column of X. For N-dimensional arrays, var operates along the first nonsingleton dimension of X. The result V is an unbiased estimator of the variance of the population from which X is drawn, as long as X consists of independent, identically distributed samples.
var normalizes V by N – 1 if N > 1, where N is the sample size. This is an unbiased estimator of the variance of the population from which X is drawn, as long as X consists of independent, identically distributed samples. For N = 1, V is normalized by 1.
V = var(X,1) normalizes by N and produces the second moment of the sample about its mean. var(X,0) is equivalent to var(X).
V = var(X,w) computes the variance using the weight vector w. The length of w must equal the length of the dimension over which var operates, and its elements must be nonnegative. If X(i) is assumed to have variance proportional to 1/w(i), then V * mean(w)/w(i) is an estimate of the variance of X(i). In other words, V * mean(w) is an estimate of variance for an observation given weight 1.
V = var(X,w,dim) takes the variance along the dimension dim of X. Pass in 0 for w to use the default normalization by N – 1, or 1 to use N.
The variance is the square of the standard deviation (STD).