Hướng dẫn python stdev vs pstdev

In this tutorial, I’ll show how to apply the stdev and pstdev functions in the Python programming language.

Table of contents:

Let’s take a look at some Python codes in action:

Creation of Example Data

We’ll use the data below as a basis for this Python programming tutorial.

my_list = [4, 1, 3, 8, 2, 7, 5, 8, 2, 7, 9, 1, 5]  # Create example list
print(my_list)                                     # Print example list
# [4, 1, 3, 8, 2, 7, 5, 8, 2, 7, 9, 1, 5]

As you can see based on the previous output of the Python console, our example data is a list object containing several integer values.

Example 1: Get Population Standard Deviation Using pstdev() Function of statistics Module

Example 1 illustrates how to calculate the population standard deviation using the pstdev function of the statistics module.

For the examples of this tutorial, we’ll first have to load the statistics module:

import statistics                                  # Import statistics

Next, we can apply the statistics.pstdev function to our example list as shown below:

print(statistics.pstdev(my_list))                  # Apply pstdev() function
# 2.7218163096852512

As you can see, the population standard deviation of our example list is 2.72.

Example 2: Get Sample Standard Deviation Using stdev() Function of statistics Module

In this example, I’ll demonstrate how to find and get the sample standard deviation of a list using the statistics module.

For this task, we can apply the stdev function (note the missing p at the beginning of the function name) to our list:

print(statistics.stdev(my_list))                   # Apply stdev() function
# 2.8329562343320847

The sample standard deviation is slightly higher than the population standard deviation that we have computed in Example 1.

Video & Further Resources

Do you need more information on the Python syntax of this tutorial? Then I recommend having a look at the following video which I have published on my YouTube channel. I illustrate the contents of this article in the video.

The YouTube video will be added soon.

In addition, you may want to read the other articles on my homepage.

• Standard Deviation in Python
• Standard Deviation by Group
• Standard Deviation of NumPy Array
• Variance in Python
• Introduction to Python

Summary: At this point you should have learned how to apply the stdev and pstdev functions of the statistics module in the Python programming language. If you have any further questions, please let me know in the comments section.

Statistics module in Python provides a function known as stdev() , which can be used to calculate the standard deviation. stdev() function only calculates standard deviation from a sample of data, rather than an entire population. 

To calculate standard deviation of an entire population, another function known as pstdev() is used. 

Standard Deviation is a measure of spread in Statistics. It is used to quantify the measure of spread, variation of a set of data values. It is very much similar to variance, gives the measure of deviation whereas variance provides the squared value. 
A low measure of Standard Deviation indicates that the data are less spread out, whereas a high value of Standard Deviation shows that the data in a set are spread apart from their mean average values. A useful property of the standard deviation is that, unlike the variance, it is expressed in the same units as the data. 

Standard Deviation is calculated by :


where x1, x2, x3.....xn are observed values in sample data,
 is the mean value of observations and
N is the number of sample observations.

Syntax : stdev( [data-set], xbar )
Parameters : 
[data] : An iterable with real valued numbers. 
xbar (Optional): Takes actual mean of data-set as value.
Returnype : Returns the actual standard deviation of the values passed as parameter.
Exceptions : 
StatisticsError is raised for data-set less than 2 values passed as parameter. 
Impossible/precision-less values when the value provided as xbar doesn’t match actual mean of the data-set. 
 

Code #1 :  

Python3

import statistics

sample = [1, 2, 3, 4, 5]

print("Standard Deviation of sample is % s "

                % (statistics.stdev(sample)))

Output : 

Standard Deviation of the sample is 1.5811388300841898 

Code #2 : Demonstrate stdev() on a varying set of data types  

Python3

from statistics import stdev

from fractions import Fraction as fr

sample1 = (1, 2, 5, 4, 8, 9, 12)

sample2 = (-2, -4, -3, -1, -5, -6)

sample3 = (-9, -1, -0, 2, 1, 3, 4, 19)

sample4 = (1.23, 1.45, 2.1, 2.2, 1.9)

print("The Standard Deviation of Sample1 is % s"

                              %(stdev(sample1)))

print("The Standard Deviation of Sample2 is % s"

                              %(stdev(sample2)))

print("The Standard Deviation of Sample3 is % s"

                              %(stdev(sample3)))

print("The Standard Deviation of Sample4 is % s"

                              %(stdev(sample4)))

Output : 

The Standard Deviation of Sample1 is 3.9761191895520196
The Standard Deviation of Sample2 is 1.8708286933869707
The Standard Deviation of Sample3 is 7.8182478855559445
The Standard Deviation of Sample4 is 0.41967844833872525

Code #3 :Demonstrate the difference between results of variance() and stdev()  

Python3

import statistics

sample = [1, 2, 3, 4, 5]

print("Standard Deviation of the sample is % s "

                    %(statistics.stdev(sample)))

print("Variance of the sample is % s"

     %(statistics.variance(sample)))

Output : 

Standard Deviation of the sample is 1.5811388300841898 
Variance of the sample is 2.5

Code #4 : Demonstrate the use of xbar parameter  

Python3

import statistics

sample = (1, 1.3, 1.2, 1.9, 2.5, 2.2)

m = statistics.mean(sample)

print("Standard Deviation of Sample set is % s"

         %(statistics.stdev(sample, xbar = m)))

Output : 

Standard Deviation of Sample set is 0.6047037842337906

Code #5 : Demonstrates StatisticsError  

Python3

import statistics

sample = [1]

print(statistics.stdev(sample))

Output : 

Traceback (most recent call last):
  File "/home/f921f9269b061f1cc4e5fc74abf6ce10.py", line 12, in 
    print(statistics.stdev(sample))
  File "/usr/lib/python3.5/statistics.py", line 617, in stdev
    var = variance(data, xbar)
  File "/usr/lib/python3.5/statistics.py", line 555, in variance
    raise StatisticsError('variance requires at least two data points')
statistics.StatisticsError: variance requires at least two data points

Applications :  

• Standard Deviation is highly essential in the field of statistical maths and statistical study. It is commonly used to measure confidence in statistical calculations. For example, the margin of error in calculating marks of an exam is determined by calculating the expected standard deviation in the results if the same exam were to be conducted multiple times.
• It is very useful in the field of financial studies as well as it helps to determine the margin of profit and loss. The standard deviation is also important, where the standard deviation on the rate of return on an investment is a measure of the volatility of the investment.