NumPy var()

import numpy as np

# create an array
array1= np.array([0, 1, 2, 3, 4, 5, 6, 7])

# calculate the variance of the array
variance = np.var(array1)

print(variance)

# Output: 5.25

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

import numpy as np

# create an array
array1 = np.array([[[0, 1], 
                    [2, 3]],                     
                   [[4, 5], 
                    [6, 7]]])

# find the variance of the entire array
variance1 = np.var(array1)

# find the variance across axis 0
variance2 = np.var(array1, 0)

# find the variance across axis 0 and 1
variance3 = np.var(array1, (0, 1))

print('\nvariance of the entire array:', variance1)
print('\nvariance across axis 0:\n', variance2)
print('\nvariance across axis 0 and 1:', variance3)

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.

import numpy as np

array1 = np.array([[1, 2, 3],
                [4, 5, 6]])

# by default int is converted to float
result1 = np.var(array1)

# get integer variance
result2 = np.var(array1, dtype = int)

print('Float variance:', result1)
print('Integer variance:', result2)

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.

import numpy as np

array1 = np.array([[1, 2, 3],
                [4, 5, 6]])

# keepdims defaults to False
result1 = np.var(array1, axis = 0)

# pass keepdims as True
result2 = np.var(array1, axis = 0, keepdims = True)

print('Dimensions in original array:', arr.ndim)
print('Without keepdims:', result1, 'with dimensions', result1.ndim)
print('With keepdims:', result2, 'with dimensions', result2.ndim)

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.

import numpy as np

array1= np.array([[1, 2, 3],
                [4, 5, 6]])

# take variance of the entire array
result1 = np.var(array1)

# variance of only even elements
result2 = np.var(array1, where = (array1% 2 == 0))

# variance of  numbers greater than 3
result3 = np.var(array1, where = (array1 > 3))

print('variance of entire array:', result1)
print('variance of only even elements:', result2)
print('variance of  numbers greater than 3:', result3)

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.

import numpy as np

array1 = np.array([[1, 2, 3],
                [4, 5, 6]])

# create an output array
output = np.zeros(3)

# compute variance and store the result in the output array
np.var(array1, out = output, axis = 0)

print('variance:', output)

Output

variance: [2.25 2.25 2.25]

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

import numpy as np

array1 = np.array([2, 4, 6, 8, 10])

# calculate variance using np.var()
variance1 = np.var(array1)

# calculate variance without using np.var()
mean = np.mean(array1)
diff_squared = (array1 - mean) ** 2
variance2 = np.mean(diff_squared)

print('variance with np.var():', variance1)
print('variance without np.var():', variance2)

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

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

import numpy as np

array1 = np.array([1, 2, 3, 4, 5])

# calculate variance with the default ddof = 0
variance0 = np.var(array1)

# calculate variance with ddof = 1
variance1 = np.var(array1, ddof = 1)

print('variance (default ddof = 0):', variance0)
print('variance (ddof = 1):', variance1)

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