numpy.var

numpy.var(a, axis=None, dtype=None, out=None, ddof=0, keepdims=<class numpy._globals._NoValue>)

Compute the variance along the specified axis.

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

Parameters:

a : array_like

Array containing numbers whose variance is desired. If a is not an array, 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 to compute 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 type the default is float32; for arrays of float types it is the same as the array type.

out : ndarray, optional

Alternate output array in which to place the result. It must have the same shape as the expected output, but the type is cast if necessary.

ddof : int, optional

“Delta Degrees of Freedom”: the divisor used in the calculation is N - ddof, where N represents the number of elements. By default ddof is zero.

keepdims : bool, optional

If this is set to True, the axes which are reduced are left in 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, then keepdims will not be passed through to the var method of sub-classes of ndarray, however any non-default value will be. If the sub-classes sum method does not implement keepdims any exceptions will be raised.

Returns:

variance : ndarray, see dtype parameter above

If out=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 as x.sum() / N, where N = len(x). If, however, ddof is specified, the divisor N - ddof is used instead. In standard statistical practice, ddof=1 provides an unbiased estimator of the variance of a hypothetical infinite population. ddof=0 provides a maximum likelihood estimate of the variance for normally distributed variables.

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

For floating-point input, the variance is computed using the same precision the input has. Depending on the input data, this can cause the results to be inaccurate, especially for float32 (see example below). Specifying a higher-accuracy accumulator using the dtype keyword 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)/2
0.2025