var

Variance

Introduction

For a given vector $x=\begin{bmatrix}x_1,x_2,\ldots,x_n\end{bmatrix}$, let $\bar{x}$ be the mean of all elements in $x$. Then, the variance can be computed by one of the following formulas:

If $x$ contains NaN, the variance $v$ will be NaN.

Usages

v = var(A)

• If A is empty, v is an empty array.
• If A is a scalar, v is equal to 0.
• If A is a vector, v is the variance of elements along the longer dimension of A.
• If A is a matrix or multi-dimensional array, elements of v are variances of vectors of A along the first non-singleton dimension.
• The variances are computed by Equation (1) above, i.e, normalised by $n-1$.

s = var(A, w)

• Same as s = var(A) above, with the input w that determines which of the above formulas will be used.
• When w == 0, it uses Equation (1). When w == 1, it uses Equation (2).

s = var(A, w, k)

• Same as s = var(A, w) above, except that elements of s correspond to vectors of A along its k-th dimension.
• k should be a real positive integer scalar.
• If k refers to a singleton dimension, v will be an array of zeros.