NumPy | var method
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NumPy's var(~) method computes the variance of values in the input array. The variance 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
var(~) method can also compute the unbiased estimate of the variance. We do this by setting ddof=1 in the parameters, as we shall see later in the examples.
Parameters
1. a | array-like
The array on which to perform the method.
2. axislink | int or tuple | optional
The axis along which we compute the variance. For 2D arrays, the allowed values are as follows:
Axis | Meaning |
|---|---|
0 | Variance will be computed column-wise |
1 | Variance will be computed row-wise |
None | Variance will be computed on a flattened array |
By default, axis=None.
3. dtype | string or type | optional
The type used to compute the variance. 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
If axis=None, then a single float representing the variance of all the values in the array is returned. Otherwise, a Numpy array is returned.
Examples
Variance of a 1D array
np.var([1,2,3,4])
1.25
Computing sample variance
To compute the sample variance, set ddof=1:
np.var([1,2,3,4], ddof=1)
1.6666666666666667
Computing population variance
To compute the population variance, leave out the ddof parameter or explicitly set ddof=0:
np.var([1,2,3,4]) # By default, ddof=0
1.25
Variance of a 2D array
Entire array
Without specifying the axis parameter, Numpy will just regard your Numpy array as a flattened array.
np.var([[1,2],[3,4]])
1.25
This code is fundamentally the same as np.var([1,2,3,4]).
Column-wise
To compute the variance column-wise, specify axis=0 in the parameters:
np.var([[1,4],[2,6], [3,8]], axis=0)
array([0.66666667, 2.66666667])
Here, we're computing the variance 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 variance column-wise, specify axis=1 in the parameters:
np.var([[1,4],[2,6], [3,8]], axis=1)
array([2.25, 4. , 6.25])
Here, we're computing three variances: 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.
