## Documentation Center |

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).

Create a matrix and find the variance along the dimensions.

X = [4 -2 1; 9 5 7] var(X,0,1) ans = 12.5000 24.5000 18.0000 var(X,0,2) ans = 9 4

Was this topic helpful?