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var(a, axis=None, dtype=None, out=None, ddof=0, keepdims=<no value>, *, where=<no value>)

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.

Notes

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

The mean is typically calculated as x.sum() / N , where N = len(x) . If, however, :None:None:`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.

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.

versionadded

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 float64 ; 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 :None:None:`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 :None:None:`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-class' method does not implement :None:None:`keepdims` any exceptions will be raised.

where : array_like of bool, optional

Elements to include in the variance. See :None:None:`~numpy.ufunc.reduce` for details.

versionadded

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.

Compute the variance along the specified axis.

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 # may vary

>>> ((1-0.55)**2 + (0.1-0.55)**2)/2
0.2025

Specifying a where argument:

>>> a = np.array([[14, 8, 11, 10], [7, 9, 10, 11], [10, 15, 5, 10]])
... np.var(a)
6.833333333333333 # may vary

>>> np.var(a, where=[[True], [True], [False]])
4.0

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

numpy.ma.core.var dask.array.reductions.var numpy.var numpy.nanstd numpy.matrixlib.defmatrix.matrix.var numpy.nanvar numpy.ma.core.MaskedArray.var pandas.core.window.expanding.Expanding.var dask.array.core.Array.var numpy.std numpy.nanmean numpy.mean pandas.core.window.rolling.Rolling.var

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