Python - How To Calculate the Standard Deviation of a List in Python

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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.

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