numpy.ma.masked_array.var¶

masked_array.var(axis=None,dtype=None,out=None,ddof=0,keepdims=<no value>)[source]¶

Compute the variance along the specified axis.

Returns the variance of the array elements, a measure of the spread of adistribution. The variance is computed for the flattened array bydefault, otherwise over the specified axis.

Parameters:

a:array_like Array containing numbers whose variance is desired. Ifa is not anarray, a conversion is attempted. axis:None or int or tuple of ints, optional Axis or axes along which the variance is computed. The default is tocompute the variance of the flattened array. New in version 1.7.0. If this is a tuple of ints, a variance is performed over multiple axes,instead of a single axis or all the axes as before. dtype:data-type, optional Type to use in computing the variance. For arrays of integer typethe default isfloat32; for arrays of float types it is the same asthe array type. out:ndarray, optional Alternate output array in which to place the result. It must havethe same shape as the expected output, but the type is cast ifnecessary. ddof:int, optional “Delta Degrees of Freedom”: the divisor used in the calculation isN-ddof, whereN represents the number of elements. Bydefaultddof 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 thevar method of sub-classes ofndarray, however any non-default value will be. If thesub-class’ method does not implementkeepdims anyexceptions will be raised.

Returns:

variance:ndarray, see dtype parameter above Ifout=None, returns a new array containing the variance;otherwise, a reference to the output array is returned.

See also

std,mean,nanmean,nanstd,nanvar

numpy.doc.ufuncs

Section “Output arguments”

Notes

The variance is the average of the squared deviations from the mean,i.e.,var=mean(abs(x-x.mean())**2).

The mean is normally calculated asx.sum()/N, whereN=len(x).If, however,ddof is specified, the divisorN-ddof is usedinstead. In standard statistical practice,ddof=1 provides anunbiased estimator of the variance of a hypothetical infinite population.ddof=0 provides a maximum likelihood estimate of the variance fornormally distributed variables.

Note that for complex numbers, the absolute value is taken beforesquaring, so that the result is always real and nonnegative.

For floating-point input, the variance is computed using the sameprecision the input has. Depending on the input data, this can causethe results to be inaccurate, especially forfloat32 (see examplebelow). Specifying a higher-accuracy accumulator using thedtypekeyword can alleviate this issue.

Examples

>>>a=np.array([[1,2],[3,4]])>>>np.var(a)1.25>>>np.var(a,axis=0)array([ 1.,  1.])>>>np.var(a,axis=1)array([ 0.25,  0.25])

In single precision, var() can be inaccurate:

>>>a=np.zeros((2,512*512),dtype=np.float32)>>>a[0,:]=1.0>>>a[1,:]=0.1>>>np.var(a)0.20250003

Computing the variance in float64 is more accurate:

>>>np.var(a,dtype=np.float64)0.20249999932944759>>>((1-0.55)**2+(0.1-0.55)**2)/20.2025