stdc#

Purpose#

Computes the sample standard deviation of the elements in each column of a matrix.

Format#

y = stdc(x)#

Parameters:: x (NxK matrix) – data
Returns:: y (Kx1 vector) – the standard deviation of each column of x.

Examples#

// Set the rng seed so that the random numbers produced will
// be repeatable
rndseed 94243524;

// Create a vector of random normal numbers
y = rndn(8100, 1);

// Compute the standard deviation of the column vector 'y'
std = stdc(y);

The standard deviation, in variable std, is equal to:

1.00183907

Remarks#

This function essentially computes sample standard deviation, s:

\[s = \frac{1}{n−1}⁢×\sum_{i=1}^n(X_i−\bar{X})^2\]

Thus, the divisor is \(N-1\) rather than \(N\), where \(N\) is the number of elements being summed.

To convert to the population’s standard deviation, multiply by \(\sqrt{\frac{n - 1}{n}}\):

\[\sigma = s*\frac{n−1}{n}\]