NumPy | std method
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NumPy's std(~) method computes the standard deviation of the values in the input array. The standard deviation is computed using the following formula:
Where,
$N$ is the size of the given array (i.e. the sample size)
$x_i$ is the value of the $i$th index in the NumPy array
$\bar{x}$ is the sample mean
The std(~) method can also compute the unbiased estimate of the standard deviation. We do this by setting ddof=1 in the parameters, as we shall see later in the examples.
Parameters
1. a | array-like
The input array.
2. axislink | int or tuple | optional
The axis along which to compute the standard deviation. For 2D arrays, the allowed values are as follows:
Axis | Meaning |
|---|---|
0 | Standard deviation will be computed column-wise |
1 | Standard deviation will be computed row-wise |
None | Standard deviation will be computed on a flattened array |
By default, axis=None.
3. dtype | string or type | optional
The type used to compute the standard deviation. If the input array is of type int, then float32 will be used. If the input array is of another numerical type, then its type will be used.
4. ddoflink | int | optional
The delta degree of freedom. This can be used to modify the denominator in the front:
By default, ddof=0.
Return value
An int representing the standard deviation of the provided values.
Examples
Standard deviation of a 1D array
np.std([1,2,3,4])
1.118
Computing sample standard deviation
To compute the sample standard deviation, set ddof=1:
np.std([1,2,3,4], ddof=1)
1.290
Computing population standard deviation
To compute the population standard deviation, leave out the ddof parameter or explicitly set ddof=0:
np.std([1,2,3,4]) # By default, ddof=0
1.118
Standard deviation of a 2D array
Entire array
Without specifying the axis parameter, NumPy will just regard your NumPy array as a flattened array.
np.std([[1,2],[3,4]])
1.118
This code is fundamentally the same as np.std([1,2,3,4]).
Column-wise
To compute the standard deviation column-wise, specify axis=0 in the parameters:
np.std([[1,4],[2,6], [3,8]], axis=0)
array([0.81649658, 1.63299316])
Here, we're computing the standard deviation of [1,2,3] (i.e. the first column) as well as [4,6,8] (i.e. the second column).
Row-wise
To compute the standard deviation column-wise, specify axis=1 in the parameters:
np.std([[1,4],[2,6], [3,8]], axis=1)
array([1.5, 2. , 2.5])
Here, we're computing three standard deviation: first row (i.e. [1,4]), second row (i.e. [2,6]) and third row (i.e. [3,8]).
Sometimes the numerical type float32 may not be accurate enough for your needs. If your application requires more accurate numbers, then set dtype=np.float64 in the argument. This will take up more memory, but will provide a more accurate result.
