# 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 )

```
1. [data]: It contains the list of data whose variance is to be calculated.
2. 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.