Computing Standard Deviation without packages in Python?

Question

I'm trying to figure out how to create a script which calculates a standard deviation for a file. As an example, say I DLed a csv with a list of values on it. I want to find the SD of these values by running a python program. We are not using numpy here!

Answer 1

If you allow the use of the standard library,

import math

xs = [0.5,0.7,0.3,0.2]     # values (must be floats!)
mean = sum(xs) / len(xs)   # mean
var  = sum(pow(x-mean,2) for x in xs) / len(xs)  # variance
std  = math.sqrt(var)  # standard deviation

If not, you need to approximate sqrt by hand. For example, you can use binary search or Newton's Method. Here's a wikipedia page for methods of doing so

Answer 2

with Python 3.4 and above there is a package called statistics, that has standard deviation (pstdev) and other functions

Here is an example of how to use it:

import statistics

data = [1, 1, 2.5, 6.5, 7.3, 8, 9.2]

print(statistics.pstdev(data))
# 3.2159043543498815

Answer 3

 from math import sqrt
 n= [11, 8, 8, 3, 4, 4, 5, 6, 6, 7, 8] 

 mean =sum(n)/len(n)
 SUM= 0
 for i in n :
     SUM +=(i-mean)**2



 stdeV = sqrt(SUM/(len(n)-1)) 
 print(stdeV)

Answer 4

filename = "C:\Users\mmb0368\Desktop\input.txt"
file = open("C:\Users\mmb0368\Desktop\input.txt","rb")

n = file.readlines()

num_list = map(lambda n: n.rstrip("\n"), n)
num_list = [int(x) for x in num_list]
mean = sum(num_list)/len(num_list)
print mean, max(num_list), min(num_list)

for snDev in num_list:

    snDev = mean**(1.0/2)
print snDev

Answer 5

from math import sqrt

def getAverage(mylist):
    """
    This function calculates the average of a list of numbers.

    Parameters:
    mylist (list): List of numbers

    Returns:
    float: Average of the numbers in the list

    Example:
    >>> getAverage([1,5,10])
    5.333333333333333
    """
    return sum(mylist)/len(mylist)

def getStandardDeviation(mylist):
    """
    This function calculates the standard deviation of a list of numbers.

    Parameters:
    mylist (list): List of numbers

    Returns:
    float: Standard deviation of the numbers in the list

    Example:
    >>> getStandardDeviation([1,5,10])
    4.509249752822894
    """
    ls=[]
    for i in mylist:
        ls.append((i - getAverage(mylist))**2)
    return sqrt( sum(ls) / (len(mylist) - 1) )

mylist = [1,5,10]

getAverage(mylist=mylist)
# 5.333333333333333

getStandardDeviation(mylist=mylist)
# 4.509249752822894

This code contains two functions getAverage and getStandardDeviation for calculating average and standard deviation of a list of numbers respectively. The getAverage function takes in a list of numbers and returns the average of those numbers. The getStandardDeviation function takes in a list of numbers and returns the standard deviation of those numbers by first finding the square difference of each number from the average and then taking the square root of the average of those squared differences. A sample list mylist of numbers is defined at the end and both functions are called with this list as argument.

Answer 6

def calculateSD(self, nums):
    n = len(nums)
    mean = sum(nums) // n
    variance = sum((x - mean) ** 2 for x in nums) / (n - 1)

    stdev = variance ** 0.5
    print(stdev)