Standard Deviation σ

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

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))

Sum : 146
Average 11.23076923076923
Variance : 4.6390532544378695
Standard Deviation 2.1538461538461537

Using Pandas

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

Using 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

Using statistics

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

Standard Deviation :  2.24179415327122