Returns the variance of all entries of the matrix specified. The variance of a set of N numbers X = [x 1 ,...,x N ] is defined as
$$ \text{var}=\frac{1}{N}\sum_{i=1}^N(x_i-\mu)^2 $$
where μ is the mean of X.
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Syntax |
Description |
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out = var(A); |
Will return variance of all of matrix A, over all dimensions. |
Example
These are some simple examples showing how to use this command.
a =[1,2,3,4,5]; ?var(a); result: 2 b =[1,2,3,4,5; 5,4,3,2,1; 1,4,2,5,8]; ?var(b); ?sum((b-mean(b))^2)/length(b); # Compare with equivalent calculation using sum and mean result: 3.55556 result: 3.55556 d = randmatrix(3,3,3); ?d; result(i,j,1): 0.345988 0.84698 0.271889 0.471725 0.316874 0.982971 0.374981 0.456099 0.2978 result(i,j,2): 0.739189 0.761315 0.5009 0.567278 0.839442 0.890164 0.19599 0.397656 0.0274667 result(i,j,3): 0.994629 0.531327 0.626759 0.572588 0.194067 0.657613 0.0505081 0.843043 0.197851 ?var(d); result: 0.0753581
See Also