## Documentation Center |

Standard deviation

`s = std(X)s = std(X,flag)s = std(X,flag,dim)`

There are two common textbook definitions for the standard deviation `s` of
a data vector `X`.

where

and *n* is the number of elements in the sample.
The two forms of the equation differ only in *n* –
1 versus *n* in the divisor.

`s = std(X)`, where `X` is
a vector, returns the standard deviation using (1) above. The result `s` is
the square root of an unbiased estimator of the variance of the population
from which `X` is drawn, as long as `X` consists
of independent, identically distributed samples.

If `X` is a matrix, `std(X)` returns
a row vector containing the standard deviation of the elements of
each column of `X`. If `X` is a
multidimensional array, `std(X)` is the standard
deviation of the elements along the first nonsingleton dimension of `X`.

`s = std(X,flag)` for `flag
= 0,` is the same as `std(X)`. For `flag
= 1`, `std(X,1)` returns the standard deviation
using (2) above, producing the second moment of the set of values
about their mean.

`s = std(X,flag,dim)` computes
the standard deviations along the dimension of `X` specified
by scalar `dim`. Set `flag` to `0` to
normalize `Y` by *n*-1; set `flag` to `1` to
normalize by *n*.

The input array, `X`, must be of type `double` or `single` for
all syntaxes.

For matrix `X`

X = 1 5 9 7 15 22 s = std(X,0,1) s = 4.2426 7.0711 9.1924 s = std(X,0,2) s = 4.000 7.5056

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