std¶

std(x: array, /, *, axis: Optional[Union[int, Tuple[int, ...]]] = None, correction: Union[int, float] = 0.0, keepdims: bool = False) array

Calculates the standard deviation of the input array `x`.

Special Cases

Let `N` equal the number of elements over which to compute the standard deviation.

• If `N - correction` is less than or equal to `0`, the standard deviation is `NaN`.

• If `x_i` is `NaN`, the standard deviation is `NaN` (i.e., `NaN` values propagate).

Parameters
• x (array) – input array. Should have a floating-point data type.

• axis (Optional[Union[int, Tuple[int, ...]]]) – axis or axes along which standard deviations must be computed. By default, the standard deviation must be computed over the entire array. If a tuple of integers, standard deviations must be computed over multiple axes. Default: `None`.

• correction (Union[int, float]) – degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the standard deviation according to `N-c` where `N` corresponds to the total number of elements over which the standard deviation is computed and `c` corresponds to the provided degrees of freedom adjustment. When computing the standard deviation of a population, setting this parameter to `0` is the standard choice (i.e., the provided array contains data constituting an entire population). When computing the corrected sample standard deviation, setting this parameter to `1` is the standard choice (i.e., the provided array contains data sampled from a larger population; this is commonly referred to as Bessel’s correction). Default: `0`.

• keepdims (bool) – if `True`, the reduced axes (dimensions) must be included in the result as singleton dimensions, and, accordingly, the result must be compatible with the input array (see Broadcasting). Otherwise, if `False`, the reduced axes (dimensions) must not be included in the result. Default: `False`.

Returns

out (array) – if the standard deviation was computed over the entire array, a zero-dimensional array containing the standard deviation; otherwise, a non-zero-dimensional array containing the standard deviations. The returned array must have the same data type as `x`.

Note

While this specification recommends that this function only accept input arrays having a floating-point data type, specification-compliant array libraries may choose to accept input arrays having an integer data type. While mixed data type promotion is implementation-defined, if the input array `x` has an integer data type, the returned array must have the default floating-point data type.