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

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

Notes

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

The average squared deviation 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 the infinite population. ddof=0 provides a maximum likelihood estimate of the variance for normally distributed variables. The standard deviation computed in this function is the square root of the estimated variance, so even with ddof=1 , it will not be an unbiased estimate of the standard deviation per se.

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

For floating-point input, the std 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

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. The default is to compute the standard deviation of the flattened array.

versionadded

If this is a tuple of ints, a standard deviation is performed over multiple 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 of integer type the default is float64, for arrays of float types it is the same as the array type.

out : ndarray, optional

Alternative output array in which to place the result. It must have the same shape as the expected output but the type (of the calculated values) will be cast if necessary.

ddof : int, optional

Means Delta Degrees of Freedom. The divisor used in calculations 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 std 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 standard deviation. See :None:None:`~numpy.ufunc.reduce` for details.

versionadded

Returns

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

Compute the standard deviation along the specified axis.

Examples

>>> a = np.array([[1, 2], [3, 4]])
... np.std(a)
1.1180339887498949 # may vary

>>> 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 # may vary

Specifying a where argument:

>>> a = np.array([[14, 8, 11, 10], [7, 9, 10, 11], [10, 15, 5, 10]])
... np.std(a)
2.614064523559687 # may vary

>>> np.std(a, where=[[True], [True], [False]])
2.0

See :

Back References

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

numpy.nanstd numpy.ma.core.MaskedArray.std pandas.core.window.rolling.Rolling.std pandas.core.generic.NDFrame._add_numeric_operations.<locals>.std dask.array.random.RandomState.lognormal dask.array.core.Array.std numpy.mean dask.array.reductions.std skimage.restoration.unwrap.unwrap_phase numpy.std numpy.ma.core.var numpy.nanvar numpy.matrixlib.defmatrix.matrix.std dask.array.random.RandomState.normal pandas.core.window.expanding.Expanding.std numpy.var dask.array.random.RandomState.gumbel numpy.ma.core.MaskedArray.var numpy.ma.core.std

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