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Manuel Scilab >> Statistiques > variance

# variance

variance of the values of a vector or matrix

### Calling Sequence

```s=variance(x[,orien[,w]])
s=variance(x,'r') or m=variance(x,1)
s=variance(x,'c') or m=variance(x,2)```

### Arguments

x

real or complex vector or matrix

orien

the orientation of the computation. Valid values or the orien parameter are 1, "r", 2 and "c".

w

w : type of normalization to use. Valid values are 0 and 1. This depends on the number of columns of x (if orien = 1 is chosen), the number of rows (if orien = 2 is chosen). If w = 0, normalizes with m-1, provides the best unbiased estimator of the variance (this is the default). If w = 1, normalizes with m, this provides the second moment around the mean. If no orien option is given, the normalization is done with n * m - 1, where n * m is the total number of elements in the matrix.

### Description

This function computes the variance of the values of a vector or matrix `x`.

For a vector or a matrix `x`, `s=variance(x)` returns in the scalar `s` the variance of all the entries of `x`.

`s=variance(x,'r')` (or, equivalently, `s=variance(x,1)`) is the rowwise variance. It returns in each entry of the row vector s the variance of each column of `x`. The generalized formulae is used, which manages complex values.

`s=variance(x,'c')` (or, equivalently, `s=variance(x,2)`) is the columnwise standard deviation. It returns in each entry of the column vector `s` the variance of each row of `x`. The generalized formulae is used, which manages complex values.

### Examples

```x=[0.2113249 0.0002211 0.6653811;0.7560439 0.4453586 0.6283918]
s=variance(x)
s=variance(x,'r')
s=variance(x,'c')```

Carlos Klimann

### Bibliography

Wonacott, T.H. & Wonacott, R.J.; Introductory Statistics, fifth edition, J.Wiley & Sons, 1990.

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