Python statistics | variance() (original) (raw)

Last Updated : 20 Mar, 2026

variance() is a function from Python’s built-in statistics module used to calculate the sample variance of a dataset. Sample variance measures how far the data values are spread from their mean. Mathematically, sample variance is calculated as:

s^2 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n - 1}

Where:

• x_i = each data value
• \bar{x} = sample mean
• n = number of data points

This function should be used when the data represents a sample, not the entire population (for population variance, use pvariance()). variance() requires at least two data points; otherwise, it raises a StatisticsError.

**Example: This example calculates the variance of a small sample dataset.

Python `

import statistics a = [4, 6, 8, 10] print(statistics.variance(a))

`

Syntax

statistics.variance(data, xbar=None)

**Parameters:

• **data: Iterable containing numeric values.
• **xbar (optional): Precomputed mean of the dataset.

**Return: Returns the sample variance of the given data.

Examples

**Example 1: This example calculates the variance of a list of floating-point numbers. The function automatically computes the mean.

Python `

import statistics d = [2.5, 3.0, 3.5, 4.0, 4.5] print(statistics.variance(d))

`

**Example 2: This example uses integer values including negative numbers to show that variance() works with different numeric types.

Python `

from statistics import variance d = (-5, -1, 0, 3, 7) print(variance(d))

`

**Example 3: This example demonstrates the use of the optional xbar parameter. We first compute the mean separately and then pass it to variance().

Python `

import statistics d = (1, 2, 3, 4, 5) m = statistics.mean(d) print(statistics.variance(d, xbar=m))

`

**Explanation: statistics.variance(d, xbar=m) uses the provided mean m instead of recalculating it internally.