Variance is the square of the standard deviation, and while it's the more fundamental statistical quantity underlying std(), it's expressed in squared units of the original data, like meters squared if the data is in meters, which makes it harder to interpret intuitively than standard deviation itself. It shares the same ddof parameter as np.std(): ddof=0, the default, computes the population variance, while ddof=1 computes the sample variance with Bessel's correction.

1Understanding np.var()

💡

Compute variance directly with np.var() rather than manually squaring the result of np.std() — it's clearer about intent and avoids the small extra floating-point rounding from an unnecessary square-then-square-root round trip.

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import numpy as np

arr = np.array([2, 4, 4, 4, 5, 5, 7, 9])
print(np.var(arr))

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2Practical Example

Here is a real-world application of np.var() showing how it is used in production NumPy code.

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import numpy as np

arr = np.array([2, 4, 4, 4, 5, 5, 7, 9])
print(np.var(arr) ** 0.5)
print(np.std(arr))

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3Best Practices

Follow these guidelines when working with np.var():

1. Use np.var() directly rather than squaring np.std()'s result manually

2. Match ddof between var() and std() calculations on the same dataset, since using different values would make the two inconsistent

3. Reach for np.std() over np.var() when you need a value in the original data's units for reporting or interpretation, reserving var() for intermediate calculations

⚠️

Tip: Compute variance directly with np.var() rather than manually squaring the result of np.std() — it's clearer about intent and avoids the small extra floating-point rounding from an unnecessary square-then-square-root round trip.

editor.html

import numpy as np

arr = np.array([2, 4, 4, 4, 5, 5, 7, 9])
print(np.var(arr))

localhost:3000

Examples

Example 01Basic Usage

import numpy as np

arr = np.array([2, 4, 4, 4, 5, 5, 7, 9])
print(np.var(arr))

Example 02Advanced Example

import numpy as np

arr = np.array([2, 4, 4, 4, 5, 5, 7, 9])
print(np.var(arr) ** 0.5)
print(np.std(arr))

Best Practices

Use np.var() directly rather than squaring np.std()'s result manually
Match ddof between var() and std() calculations on the same dataset, since using different values would make the two inconsistent
Reach for np.std() over np.var() when you need a value in the original data's units for reporting or interpretation, reserving var() for intermediate calculations

Interview Question

Why is variance measured in 'squared units' of the original data, and how does standard deviation address that?▼

Hint: Think about the arithmetic that computes variance.

Variance is computed by averaging the squared difference between each value and the mean — squaring is what makes all the differences positive so they don't cancel out when averaged, but it also means the result's units get squared along with the values, like meters becoming meters squared. Standard deviation is defined as the square root of variance specifically to undo that squaring and bring the result back into the same units as the original data, which is why standard deviation is generally more intuitive to interpret directly, while variance remains more convenient for certain mathematical manipulations.

Exercises

MediumPractice using np.var() in a real scenario.

View Solution

import numpy as np

arr = np.array([2, 4, 4, 4, 5, 5, 7, 9])
print(np.var(arr))

Frequently Asked Questions

Why is variance measured in 'squared units' of the original data, and how does standard deviation address that?▼

Related Functions

np-stdnp-meannp-corrcoef