MATLAB Function Reference

std

Standard deviation

Syntax

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

Definition

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 versus in the divisor.

Description

s = std(X), where X is a vector, returns the standard deviation using (1) above. If X is a random sample of data from a normal distribution, s² is the best unbiased estimate of its variance.

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 th 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 sample about its mean.

s = std(X,flag,dim) computes the standard deviations along the dimension of X specified by scalar dim.

Examples

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

See Also

corrcoef, cov, mean, median

startup

stem