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.
a : array_like
axis : int, optional
dtype : data-type, optional
out : ndarray, optional
ddof : int, optional
keepdims : bool, optional
variance : ndarray, see dtype parameter above
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.
>>> 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) 0.20405951142311096
Computing the variance in float64 is more accurate:
>>> np.var(a, dtype=np.float64) 0.20249999932997387 >>> ((1-0.55)**2 + (0.1-0.55)**2)/2 0.20250000000000001