NumPy var()

var() Syntax

The syntax of the numpy.var() method is:

numpy.var(array, axis = None, dtype = None, out = None, ddof = 0, keepdims = <no value>, where = <no value>)

var() Arguments

The numpy.var() method takes the following arguments:

• array - array containing numbers whose variance is desired (can be array_like)
• axis (optional) - axis or axes along which the variances are computed (int or tuple of int)
• dtype (optional) - the data type to use in the calculation of variance (datatype)
• out (optional) - output array in which to place the result (ndarray)
• ddof (optional) - delta degrees of freedom (int)
• keepdims (optional) - specifies whether to preserve the shape of the original array (bool)
• where (optional) - elements to include in the variance (array of bool)

var() Return Value

The numpy.var() method returns the variance of the array.

Example 1: Find the variance of an ndArray

Output

variance of the entire array: 5.25

variance across axis 0:
 [[4. 4.]
 [4. 4.]]

variance across axis 0 and 1: [5. 5.]

Example 2: Specifying the Data Type of Variance of an ndArray

The dtype parameter can be used to control the data type of the output array.

Output

Float variance: 2.9166666666666665
Integer variance: 3

Note: Using a lower precision dtype, such as int, can lead to a loss of accuracy.

Example 3: Using Optional keepdims Argument

If keepdims is set to True, the resultant variance array is of the same number of dimensions as the original array.

Output

Dimensions in original array: 2
Without keepdims: [2.25 2.25 2.25] with dimensions 1
With keepdims: [[2.25 2.25 2.25]] with dimensions 2

Example 4: Using Optional where Argument

The optional argument where specifies which elements to include in the variance.

Output

variance of entire array: 2.9166666666666665
variance of only even elements: 2.6666666666666665
variance of  numbers greater than 3: 0.6666666666666666

Example 5: Using Optional out Argument

The out parameter allows us to specify an output array where the result will be stored.

Output

variance: [2.25 2.25 2.25]

var = sum((array1 - arr.mean())** 2) / (N - 1)

variance with np.var(): 8.0
variance without np.var(): 8.0

var = sum((array1 - arr.mean())** 2) / (N - ddof)

variance (default ddof = 0): 2.0
variance (ddof = 1): 2.5