# Python | Standard deviation of list

• Last Updated : 17 Jan, 2023

Sometimes, while working with Mathematics, we can have a problem in which we intend to compute the standard deviation of a sample. This has many applications in competitive programming as well as school level projects. Let’s discuss certain ways in which this task can be performed.
Method #1 : Using sum() + list comprehension This is a brute force shorthand to perform this particular task. We can approach this problem in sections, computing mean, variance and standard deviation as square root of variance. The sum() is key to compute mean and variance. List comprehension is used to extend the common functionality to each of element of list.

## Python3

 `# Python3 code to demonstrate working of``# Standard deviation of list``# Using sum() + list comprehension` `# initializing list``test_list ``=` `[``4``, ``5``, ``8``, ``9``, ``10``]` `# printing list``print``(``"The original list : "` `+` `str``(test_list))` `# Standard deviation of list``# Using sum() + list comprehension``mean ``=` `sum``(test_list) ``/` `len``(test_list)``variance ``=` `sum``([((x ``-` `mean) ``*``*` `2``) ``for` `x ``in` `test_list]) ``/` `len``(test_list)``res ``=` `variance ``*``*` `0.5` `# Printing result``print``(``"Standard deviation of sample is : "` `+` `str``(res))`

Output

```The original list : [4, 5, 8, 9, 10]
Standard deviation of sample is : 2.3151673805580453
```

Method #2 : Using pstdev() This task can also be performed using inbuilt functionality of pstdev(). This function computes standard deviation of sample internally.

## Python3

 `# Python3 code to demonstrate working of``# Standard deviation of list``# Using pstdev()``import` `statistics` `# initializing list``test_list ``=` `[``4``, ``5``, ``8``, ``9``, ``10``]` `# printing list``print``(``"The original list : "` `+` `str``(test_list))` `# Standard deviation of list``# Using pstdev()``res ``=` `statistics.pstdev(test_list)` `# Printing result``print``(``"Standard deviation of sample is : "` `+` `str``(res))`

Output

```The original list : [4, 5, 8, 9, 10]
Standard deviation of sample is : 2.3151673805580453
```

Method #3 : Using numpy library

## Note: Install numpy module using command “pip install numpy”

Another approach to calculate the standard deviation of a list is by using the numpy library. The numpy library provides a function called std() which can be used to calculate the standard deviation of a list.

## Python3

 `# Python3 code to demonstrate working of``# Standard deviation of list``import` `numpy as np``# initializing list``test_list ``=` `[``4``, ``5``, ``8``, ``9``, ``10``]``res ``=` `np.std(test_list)``# printing list``print``(res)`

Output:

2.3151673805580453

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