Python program to find standard deviation

Last update on August 19 2022 21:51:39 (UTC/GMT +8 hours)

Python Math: Exercise-57 with Solution

Write a Python program to calculate the standard deviation of the following data.

Sample Solution:-

Python Code:

import math
import sys

def sd_calc(data):
    n = len(data)

    if n <= 1:
        return 0.0

    mean, sd = avg_calc(data), 0.0

    # calculate stan. dev.
    for el in data:
        sd += (float(el) - mean)**2
    sd = math.sqrt(sd / float(n-1))

    return sd

def avg_calc(ls):
    n, mean = len(ls), 0.0

    if n <= 1:
        return ls[0]

    # calculate average
    for el in ls:
        mean = mean + float(el)
    mean = mean / float(n)

    return mean

data = [4, 2, 5, 8, 6]
print("Sample Data: ",data)
print("Standard Deviation : ",sd_calc(data))

Sample Output:

Sample Data:  [4, 2, 5, 8, 6]                                                                                 
Standard Deviation :  2.23606797749979

Pictorial Presentation:

Python program to find standard deviation

Flowchart:

Python program to find standard deviation

Python Code Editor:

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Python: Tips of the Day

Intersect Sets:

To get what's common in two sets:

a = {1,2,3}
b = {3,4,5}
c = a.intersection(b)

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 :

Python program to find standard deviation
where x1, x2, x3.....xn are observed values in sample data,
Python program to find standard deviation
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.

How do you find the mean and standard deviation of data in Python?

The standard deviation is the square root of the average of the squared deviations from the mean, i.e., std = sqrt(mean(x)) , where x = abs(a - a. mean())**2 . The average squared deviation is typically calculated as x. sum() / N , where N = len(x) .

How do you find standard deviation in Python without libraries?

To calculate the standard deviation, let's first calculate the mean of the list of values. The mean comes out to be six (μ = 6). Now, to calculate the standard deviation, using the above formula, we sum the squares of the difference between the value and the mean and then divide this sum by n to get the variance.

How does Python Numpy calculate standard deviation?

The numpy module of Python provides a function called numpy. std(), used to compute the standard deviation along the specified axis. This function returns the standard deviation of the array elements. The square root of the average square deviation (computed from the mean), is known as the standard deviation.

How does Python calculate standard variance?

Steps to Finding Variance.
Find a mean of the set of data..
Subtract each number from a mean..
Square the result..
Add the results together..
Divide a result by the total number of numbers in the data set..