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 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. 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 sample about its 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.

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, var

startup

stem

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