Python Variance: How To Calculate Variance In Python 2023

In mathematics and statistics, variance is a measure of the spread of a set of values. It is computed as the average squared deviation of a set of values from their mean. This blog will go through the process of calculating variance in Python.

Variance is a measure of the degree of disagreement among set of data points. Variance is calculated by the variance() function in Python statistics module provides potent tools which can be used to compute anything related to Statistics.

Variance is a measure of dispersion in a set of numbers which is useful when you have to compare different sets of numbers. It is a measure of the amount by which each number in a data set varies from the mean. It may sound complicated but the function variance() can be used for this purpose. This blog will help you understand how variance() can be used to calculate variance in python.

The variance() function is a built-in function that calculates the variance from the sample of data (sample is a subset of populated data). The variance() function is provided by the Python statistics module, and can be used to compute anything related to Statistics. This blog will explain the variance() function and the syntax that is used to calculate the variance.

Syntax:

statistics.variance(data, xbar=None)

import statistics

dataset = [21, 19, 11, 21, 19, 46, 29]

output = statistics.variance(dataset) 

print(output)

OUTPUT:

124.23809523809524

Python variance() with both Arguments:

Variance is a measure of how spread out the values in a set or population are. For example, the standard deviation is a measure of how spread out the values in a probability distribution.One of the most common statistical tools is the computation of variance. Variance is a measure which is used to assess the difference between a population or a sample and its expected value. It is calculated by the standard deviation and can be expressed as a ratio. Python provides powerful tools that can be used to achieve any purpose related to statistics. One of these tools is the variance() that is a built-in function used to calculate the variance from the sample of data.

import statistics

dataset = [21, 19, 11, 21, 19, 46, 29]

meanValue = statistics.mean(dataset)

output = statistics.variance(dataset, meanValue) 

print(output)

OUPUT:

 124.23809523809524

Calculate variance() of Fraction:

The result of the variance is the standard deviation of the mean. The result of the standard deviation is the square root of the variance, which is the square root of the standard deviation.The variance() (or variance) is a built-in function provided by the Python statistics module. The variance tells you about the spread of the sample data and is used to determine the standard deviation of the sample mean.

The standard deviation is one of the most common statistics used in the social sciences. Its definition is the square root of the variance of a sample. The standard deviation is how spread out the values are in a data set.

from decimal import Decimal as D

from statistics import variance
 
print(variance([D("21.11"), D("19.21"), D("46.21"), D("18.21"), D("29.21"), D("21.06")]))

OUTPUT:

114.73775

Compute the Variance in Python using Numpy:

“In statistics, the variance of a random variable is the average of the squared deviations of the random variable from its mean. This can be calculated by taking the average of the squared deviations of the random variable from its mean, or by taking the square root of the average of the squared deviations of the random variable from its mean.”The variance() is a built-in function to calculate the standard deviation of the sample mean.Standard deviation is a measure of how spread out the data is. To calculate the standard deviation of the sample mean

import numpy as np

dataset= [21, 11, 19, 18, 29, 46, 20]

variance= np.var(dataset)

print(variance)

OUTPUT:

108.81632653061224

Coding a variance() Function in Python:

The variance in Python is calculated by the variance() function. The standard deviation of the sample mean is computed by the standard deviation() function.The mean is the sum of all the values in a data set divided by the number of values. The standard deviation is the average of the squared deviations of each value from the mean. The variance() function calculates the standard deviation of the mean, that is, the sample standard deviation.The standard deviation of the sample mean is the square root of variance of the sample mean.The standard deviation is the square root of variance.

Example #1:

def variance(data):

     # Number of observations
     n = len(data)

     # Mean of the data
     mean = sum(data) / n

     # Square deviations
     deviations = [(x - mean) ** 2 for x in data]

     # Variance
     variance = sum(deviations) / n

     return variance

variance([4, 8, 6, 5, 3, 2, 8, 9, 2, 5])

OUTPUT:

5.76

Example #2:

def variance(data, ddof=0):

     n = len(data)

     mean = sum(data) / n

     return sum((x - mean) ** 2 for x in data) / (n - ddof)

variance([4, 8, 6, 5, 3, 2, 8, 9, 2, 5])

#Output - 5.76

variance([4, 8, 6, 5, 3, 2, 8, 9, 2, 5], ddof=1)

#Output - 6.4

Using Python’s pvariance() and variance():

Python Variance is a built-in function that is used to calculate the variance from the sample of data (sample is a subset of populated data). This blog will explore the concept of variance and describes the sample variance/population variance in Python.The variance() function can only be applied on a sample of data so it is most useful for small sets of data. Given the input, the variance() will compute the variance. The variance is defined as the average squared deviation about the mean of the data. Given a set of data, you will be able to compute the average and the variance.

“Variance” is defined as the ratio of the standard deviation to the mean. You calculate it the same way you’d calculate the standard deviation.

Example #1:

import statistics

statistics.pvariance([4, 8, 6, 5, 3, 2, 8, 9, 2, 5])

#Output - 5.760000000000001

Example #2:

import statistics

statistics.variance([4, 8, 6, 5, 3, 2, 8, 9, 2, 5])

#Output - 6.4

Calculating the Standard Deviation:

Variance is the difference between a set of data and their arithmetic mean. It is a measure of dispersion or spread in a data set. It is commonly used to describe the amount of uncertainty in a given variable, or the standard deviation of a variable.Variance is a statistical measure of dispersion about a central value. It is the difference between the mean of the sample and the average of the values that compose the sample. It is useful in building predictive models or when trying to find a pattern in a sequence of numbers.

Example #1:

import math

# We relay on our previous implementation for the variance
def variance(data, ddof=0):
     n = len(data)
     mean = sum(data) / n
     return sum((x - mean) ** 2 for x in data) / (n - ddof)


def stdev(data):
     var = variance(data)
     std_dev = math.sqrt(var)
     return std_dev

stdev([4, 8, 6, 5, 3, 2, 8, 9, 2, 5])

OUTPUT:

2.4

Example #2:

def stdev(data, ddof=0):
     return math.sqrt(variance(data, ddof))

stdev([4, 8, 6, 5, 3, 2, 8, 9, 2, 5])
#Output - 2.4

stdev([4, 8, 6, 5, 3, 2, 8, 9, 2, 5], ddof=1)
#Output - 2.5298221281347035

Using Python’s pstdev() and stdev():

Variance is the measure of the dispersion of a set of numbers. In the simplest case, it is the set of numbers that appear in the data set. Normal distribution is the most common example of variance. But in the real world, variance can vary.Variance is a measure of dispersion. A measure of dispersion is a statistic that can be estimated from a set of data. It is the average of the squared deviations, divided by the mean. It measures deviations of a particular variable from the central tendency of the entire set of data.

Example #1:

import statistics

statistics.pstdev([4, 8, 6, 5, 3, 2, 8, 9, 2, 5])
#Output - 2.4000000000000004

statistics.stdev([4, 8, 6, 5, 3, 2, 8, 9, 2, 5])
#Output - 2.5298221281347035

Example #2:

import numpy as np

def get_variance(xs):
    mean = np.mean(xs)
    summed = 0
    for x in xs:
        summed += (x - mean)**2
    return summed / (len(xs))

print(get_variance([1,2,3,4,5]))

OUTPUT:

2.0

The variance() is a built-in function used to compute the variance from the sample of data (sample is a subset of populated data). Python statistics module provides potent tools which can be used to compute anything related to Statistics. The variance() is one such function.The Python Variance() function is used to calculate the variance of a statistic. The function is overloaded and can be used to calculate the variance of many different populations. The variance() function is actually a built-in function in Python. There is a lot of information that can be obtained with the Python statistics module which is provided by the Python interpreter. One such function is the variance() function.

The built-in function called variance() is used to calculate the variance from the sample of data. Python statistics module provides potent tools which can be used to compute anything related to Statistics. The variance() is one such function.

Example #3:

import numpy as np

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

variance = np.var(a, ddof=1)

print(variance)

#Output - 2.5

Example #4:

results=[-14.82381293, -0.29423447, -13.56067979, -1.6288903, -0.31632439,
      0.53459687, -1.34069996, -1.61042692, -4.03220519, -0.24332097]

import numpy as np
print('numpy variance: ', np.var(results))


# without numpy by hand  

# there are two ways of calculating the variance 
#   - 1. direct as central 2nd order moment (https://en.wikipedia.org/wiki/Moment_(mathematics))divided by the length of the vector
#   - 2. "mean of square minus square of mean" (see https://en.wikipedia.org/wiki/Variance)

# calculate mean
n= len(results)
sum=0
for i in range(n):
    sum = sum+ results[i]


mean=sum/n
print('mean: ', mean)

#  calculate the central moment
sum2=0
for i in range(n):
    sum2=sum2+ (results[i]-mean)**2

myvar1=sum2/n
print("my variance1: ", myvar1)

# calculate the mean of square minus square of mean
sum3=0
for i in range(n):
    sum3=sum3+ results[i]**2

myvar2 = sum3/n - mean**2
print("my variance2: ", myvar2)

OUTPUT:

numpy variance:  28.8223642606
mean:  -3.731599805
my variance1:  28.8223642606
my variance2:  28.8223642606

Python variance() is a built-in function which can be used to calculate the variance, which is an important statistical tool. Variance is the measure of dispersion in a set of data, typically used to assess the variability of values in a sample. It is a statistical measurement that indicates how spread out the values in a set of data are.

Example #5:

vac_nums = [0,0,0,0,0, 1,1,1,1,1,1,1,1, 2,2,2,2, 3,3,3 ] #your code goes here

mean = sum(vac_nums)/len(vac_nums)

count=0

for i in range(len(vac_nums)):
   variance = (vac_nums[i]-mean)**2
   count += variance

print(count/len(vac_nums))

#Output- 0.9875

Conclusion:

If you’re new to Data Science, you may wonder how to calculate variance in Python. Variance is a measure of dispersion, which is the degree to which a data point differs from the mode. The variance or standard deviation of a data set is a measure of how far values are spread out from the mean.The variance() method of Statistics object in Python is often overlooked. A lot of people go ahead and use other methods for calculating the variance, like the mean() and std() methods. But the variance() function has a lot of desirable properties, like the ability to return a list of numbers, the ability to return a single number, and the ability to return multiple numbers.Variance() function is built-in function of the Python statistics module. The functions of this module can be used to compute many different statistics, like mean, standard deviation, and others. The variance() function can be used to calculate the variance from the sample of data. Variance is one of the statistics calculated by the Python statistics module.