function to calculate Standard Deviation of a list or set of numbers in Python

Find out the average value (μ ) of the numbers or the list
Find out the sum (Σ) of square of difference between number and average value
Divide the sum by number of elements ( N )
Take the square root of the above division

We will create a Python function to return the Standard Deviation.
Note that this is Population Standard Deviation

import math
list1=[12,13,15,11,9,12,13,10,11,12,13,7,8]
def my_stddev(my_list):
    my_sum=0
    for i in my_list:
        my_sum=my_sum+i
    #print(my_sum)
    print("Sum :",my_sum)
    my_no=len(my_list)
    
    my_avg=my_sum/my_no
    print("Average",my_avg)
    sum_avg=0.0
    for i in my_list:
        sum_avg=sum_avg+math.pow((i-my_avg),2)
    my_variance = sum_avg/my_no
    print("Variance :",my_variance )    
    std=math.sqrt(my_variance)
    return std
  
print("Standard Deviation",my_stddev(list1))

Output

Sum : 146
Average 11.23076923076923
Variance : 4.6390532544378695
Standard Deviation 2.1538461538461537

We will compare the Standard Deviation values by using Pandas, Numpy and Python statistics library. Note the difference in values as there are two different formulas to get the Standard Deviation. The Population method uses N and Sample method uses N - 1, where N is the total number of elements.

Using Pandas

Read more on Pandas here. We can use ddof option to tell Delta Degrees of Freedom. Default value of ddof is 1. The code with output is here.

list1=[12,13,15,11,9,12,13,10,11,12,13,7,8]
my_dict={'l1':list1}
my_data = pd.DataFrame(data=my_dict)
print(my_data['l1'].std(ddof=0))  # 2.1538461538461537
print(my_data['l1'].std(ddof=1))  # 2.24179415327122

Note that we are getting the same value in Python and Pandas by using ddof=0 in Pandas std() function.

Using Numpy

Read more on Numpy here. There is a built in standar deviation function in Numpy.

import numpy as np
my_data=np.array(list1)
print(my_data.std(ddof=0)) # 2.153846153846154
print(my_data.std(ddof=1)) # 2.2417941532712202

Here also we are getting same value as Python by using ddof=0

Using statistics

We will use the statistics library

import statistics 
print("Standard Deviation : ",statistics.stdev(list1))

Output is here

Standard Deviation :  2.24179415327122

The statistics library uses sample Standar Deviation.

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Subhendu Mohapatra

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Standard Deviation σ

Using Pandas

Using Numpy

Using statistics

Subhendu Mohapatra