# astd¶

## Purpose¶

Computes the standard deviation of the elements across one dimension of an N-dimensional array.

## Format¶

y = astd(x, dim)
Parameters:
• x (N-dimensional array) –

• dim (scalar) – number of dimension to sum across.

Returns:

y (N-dimensional array) – standard deviation across specified dimension of x.

## Examples¶

/*
** Create a 1e6x1 vector of random normal numbers with a
** standard deviation of 25 and reshape it into a
** 2e5x3x2 array
*/
rndseed 456;
a = areshape(25*rndn(2e6, 1), 2e5|3|2);
y = astd(a, 3);


The code above should produce a 3x2 matrix with all elements close to 25 similar to what we see below.

25.070091        24.994774
24.988263        24.990370
24.956467        24.987882


## Remarks¶

The output y, will have the same sizes of dimensions as x, except that the dimension indicated by dim will be collapsed to 1.

For each column, this function essentially computes sample standard deviation, s:

$s = \sqrt{\frac{1}{n−1⁢}×\Sigma_{i=1}^n(X_i − \bar{X})^2}$

Thus, the divisor is N-1 rather than N, where N is the number of elements being summed. See astds() for the alternate definition.