Calculate the Standard Deviation of a List in Python

Lakshay Kapoor Jul 13, 2021 Jun 17, 2021

In Python, there are a lot of statistical operations being carried out. One of these operations is calculating the standard deviation of a given data. The standard deviation of data tells us how much the data has deviated from the mean value. Mathematically, the standard deviation is equal to the square root of variance.

This tutorial will demonstrate how to calculate the standard deviation of a list in Python.

Use the `pstdev()` Function of the `statistics` Module to Calculate the Standard Deviation of a List in Python

The `pstdev()` function is one of the commands under Python’s `statistics` module. The `statistics` module provides functions to perform statistical operations like mean, median, and standard deviation on numeric data in Python.

The `pstdev()` function of the `statistics` module helps a user to calculate the standard deviation of the whole population.

``````import statistics

list = [12, 24, 36, 48, 60]
print("List : " + str(list))

st_dev = statistics.pstdev(list)
print("Standard deviation of the given list: " + str(st_dev))
``````

Output:

``````List : [12, 24, 36, 48, 60]
Standard deviation of the given list: 16.97056274847714
``````

In the above example, the `str()` function converts the whole list and its standard deviation into a string because it can only be concatenated with a string.

Use the `std()` Function of the `NumPy` Library to Calculate the Standard Deviation of a List in Python

The `NumPy` stands for `Numerical Python` is a widely used library in Python. This library helps in dealing with arrays, matrices, linear algebra, and Fourier transform.

The `std()` function of the `NumPy` library is used to calculate the standard deviation of the elements in a given array(list). Check the example below.

``````import numpy as np

list = [12, 24, 36, 48, 60]
print("List : " + str(list))

st_dev = np.std(list)

print("Standard deviation of the given list: " + str(st_dev))
``````

Output:

``````List : [12, 24, 36, 48, 60]
Standard deviation of the given list: 16.97056274847714
``````

Use the `sum()` Function and List Comprehension to Calculate the Standard Deviation of a List in Python

As the name suggests, the `sum()` function provides the sum of all the elements of an iterable, like lists or tuples. The list comprehension is a method of creating a list from the elements present in an already existing list.

The `sum()` function and list comprehension can help calculate the standard deviation of a list. Here’s an example code.

``````import math

list= [12, 24, 36, 48, 60]
print("List : " + str(list))

mean = sum(list) / len(list)
var = sum((l-mean)**2 for l in list) / len(list)
st_dev = math.sqrt(var)

print("Standard deviation of the given list: " + str(st_dev))
``````

Output:

``````List : [12, 24, 36, 48, 60]
Standard deviation of the given list: 16.97056274847714
``````

In the example above, the `math` module is imported. It provides the `sqrt()` function to calculate the square root of a given value. Also, note that the function `len()` is also used. This function helps provide the length of the given list, for example, the number of elements in the list.

This method is based on the mathematical formula of standard deviation. First, we calculate the variance and then get its square root to find the standard deviation.

Lakshay Kapoor is a final year B.Tech Computer Science student at Amity University Noida. He is familiar with programming languages and their real-world applications (Python/R/C++). Deeply interested in the area of Data Sciences and Machine Learning.