How to Use var in NumPy: Calculate Variance Easily

Use numpy.var() to calculate the variance of array elements. It measures how spread out numbers are by default over the entire array, with options to specify axis and data type.

Syntax

The numpy.var() function calculates the variance of array elements. Here is the syntax:

• numpy.var(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False)

Parameters explained:

• a: Input array to calculate variance on.
• axis: Axis or axes along which to compute variance. Default is None (whole array).
• dtype: Data type for computation (e.g., float64).
• out: Optional output array to store result.
• ddof: Delta degrees of freedom. Variance divisor is N - ddof. Default is 0.
• keepdims: If True, keeps reduced dimensions for broadcasting.

python

numpy.var(a, axis=None, dtype=None, out=None, ddof=0, keepdims=False)

Example

This example shows how to calculate variance of a 1D and 2D NumPy array. It demonstrates default behavior and variance along an axis.

python

import numpy as np

# 1D array variance
arr1 = np.array([1, 2, 3, 4, 5])
var1 = np.var(arr1)

# 2D array variance over entire array
arr2 = np.array([[1, 2, 3], [4, 5, 6]])
var2 = np.var(arr2)

# Variance along axis 0 (columns)
var_axis0 = np.var(arr2, axis=0)

# Variance along axis 1 (rows)
var_axis1 = np.var(arr2, axis=1)

print(f"Variance of arr1: {var1}")
print(f"Variance of arr2 (all elements): {var2}")
print(f"Variance of arr2 along axis 0: {var_axis0}")
print(f"Variance of arr2 along axis 1: {var_axis1}")

Output

Variance of arr1: 2.0
Variance of arr2 (all elements): 2.9166666666666665
Variance of arr2 along axis 0: [2.25 2.25 2.25]
Variance of arr2 along axis 1: [0.66666667 0.66666667]

Common Pitfalls

Common mistakes when using numpy.var() include:

• Forgetting that variance divides by N by default, not N-1. Use ddof=1 for sample variance.
• Not specifying axis when working with multi-dimensional arrays, leading to variance over the whole array instead of per row/column.
• Using integer arrays without specifying dtype, which can cause integer division and incorrect results.

python

import numpy as np

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

# Wrong: sample variance expected but default ddof=0 used
var_wrong = np.var(arr)

# Right: sample variance with ddof=1
var_right = np.var(arr, ddof=1)

print(f"Default variance (ddof=0): {var_wrong}")
print(f"Sample variance (ddof=1): {var_right}")

Output

Default variance (ddof=0): 2.0
Sample variance (ddof=1): 2.5

Quick Reference

Summary tips for using numpy.var():

• Use axis to control dimension of variance calculation.
• Set ddof=1 for sample variance.
• Specify dtype=float64 for precise results on integer arrays.
• keepdims=True helps keep array shape for broadcasting.

Key Takeaways

Use numpy.var() to calculate variance of array elements easily.

Set axis parameter to compute variance along specific dimensions.

Use ddof=1 for sample variance instead of population variance.

Specify dtype=float64 to avoid integer division errors.

Keepdims=True preserves array shape after variance calculation.