# How to calculate variance of a list in Python without NumPy

In this article, we will learn how to calculate the **variance** of a list in Python using different methods.

## Variance

- Variance is an important mathematical tool used in statistics. It is used to handle large amounts of data.
- It is the square of the standard deviation for a given data set.
- Variance is also known as the second central moment of a distribution.
- It is calculated by the mean of the square minus square of the mean of a given data set.
- Formula:

Var(X)= E[(X- μ )^2]

You can check this out: Find variance of a list in Python using NumPy

### Syntax: Python variance()

Python provides an inbuilt function to calculate the variance of a list. The syntax is given below along with the explanation of its parameters.

variance( [data], mean )

- [data]: It contains the list of data whose variance is to be calculated.
- mean: It is an optional parameter. It takes the value of the actual mean.

## Rudimentary method to calculate variance of a list in Python

This is the simplest method used to calculate the variance of a list. In the example given below, we calculate the mean and then using the formula given above, we calculate the variance.

No inbuilt function is used in this.

list1 = [10, 20, 30, 40, 50, 60] print("The original list is : " + str(list1)) length= int(len(list1)) mean = sum(list1) / length ans = sum((i - mean) ** 2 for i in list1) / length print("The variance of list is : " + str(ans))

Output:

The original list is : [10, 20, 30, 40, 50, 60] The variance of list is : 291.6666666666667

## Variance of a list using inbuilt function

Example 1: In this example, we use the inbuilt function but the optional parameter i.e. mean is not mentioned. This function makes it very easy to calculate the variance of a given data set.

import statistics list1 = [10, 70, 30, 90, 20, 30] print("The original list is : " + str(list1)) ans = statistics.variance(list1) print("The variance of list is : " + str(ans))

Output:

The original list is : [10, 70, 30, 90, 20, 30] The variance of list is : 976.6666666666666

Example 2: In this, we use the inbuilt function. We mention both the parameters in it.

import statistics list1 = (1, 1.2, 1.3, 1.4, 1.5, 1.6) mean = statistics.mean(list1) print("Variance of Sample set is % s" %(statistics.variance(list1, xbar = mean)))

Output:

Variance of Sample set is 0.046666666666666676

These are the ways to easily calculate the variance of a given list.

## Leave a Reply