numpy.std¶

numpy.std(a,axis=None,dtype=None,out=None,ddof=0,keepdims=<class numpy._globals._NoValue>)[source]¶

Compute the standard deviation along the specified axis.

Returns the standard deviation, a measure of the spread of a distribution,of the array elements. The standard deviation is computed for theflattened array by default, otherwise over the specified axis.

Parameters:

a : array_like Calculate the standard deviation of these values. axis : None or int or tuple of ints, optional Axis or axes along which the standard deviation is computed. Thedefault is to compute the standard deviation of the flattened array. New in version 1.7.0. If this is a tuple of ints, a standard deviation is performed overmultiple axes, instead of a single axis or all the axes as before. dtype : dtype, optional Type to use in computing the standard deviation. For arrays ofinteger type the default is float64, for arrays of float types it isthe same as the array type. out : ndarray, optional Alternative output array in which to place the result. It must havethe same shape as the expected output but the type (of the calculatedvalues) will be cast if necessary. ddof : int, optional Means Delta Degrees of Freedom. The divisor used in calculationsisN-ddof, whereN represents the number of elements.By defaultddof is zero. keepdims : bool, optional If this is set to True, the axes which are reduced are leftin the result as dimensions with size one. With this option,the result will broadcast correctly against the input array. If the default value is passed, thenkeepdims will not bepassed through to thestd method of sub-classes ofndarray, however any non-default value will be. If thesub-classessum method does not implementkeepdims anyexceptions will be raised.

Returns:

standard_deviation : ndarray, see dtype parameter above. Ifout is None, return a new array containing the standard deviation,otherwise return a reference to the output array.

See also

var,mean,nanmean,nanstd,nanvar

numpy.doc.ufuncs

Section “Output arguments”

Notes

The standard deviation is the square root of the average of the squareddeviations from the mean, i.e.,std=sqrt(mean(abs(x-x.mean())**2)).

The average squared deviation is normally calculated asx.sum()/N, whereN=len(x). If, however,ddof is specified,the divisorN-ddof is used instead. In standard statisticalpractice,ddof=1 provides an unbiased estimator of the varianceof the infinite population.ddof=0 provides a maximum likelihoodestimate of the variance for normally distributed variables. Thestandard deviation computed in this function is the square root ofthe estimated variance, so even withddof=1, it will not be anunbiased estimate of the standard deviation per se.

Note that, for complex numbers,std takes the absolutevalue before squaring, so that the result is always real and nonnegative.

For floating-point input, thestd is computed using the sameprecision the input has. Depending on the input data, this can causethe results to be inaccurate, especially for float32 (see example below).Specifying a higher-accuracy accumulator using thedtype keyword canalleviate this issue.

Examples

>>>a=np.array([[1,2],[3,4]])>>>np.std(a)1.1180339887498949>>>np.std(a,axis=0)array([ 1.,  1.])>>>np.std(a,axis=1)array([ 0.5,  0.5])

In single precision, std() can be inaccurate:

>>>a=np.zeros((2,512*512),dtype=np.float32)>>>a[0,:]=1.0>>>a[1,:]=0.1>>>np.std(a)0.45000005

Computing the standard deviation in float64 is more accurate:

>>>np.std(a,dtype=np.float64)0.44999999925494177