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Understanding Types of Means | Set 1

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  • Last Updated : 30 Jul, 2021

It is one of the most important concepts of statistics, a crucial subject to learn Machine Learning. 
 

  • Arithmetic Mean : It is the mathematical expectation of a discrete set of numbers or average. 
    Denoted by , pronounced as “x-bar”. It is the sum of all the discrete values in the set divided by the total number of values in the set. 
    The formula to calculate the mean of n values – x1, x2, ….. xn 
     

  • Example – 
Sequence = {1, 5, 6, 4, 4}

Sum             = 20
n, Total values = 5
Arithmetic Mean = 20/5 = 4
  • Code – 

Python3




# Arithmetic Mean
 
import statistics
 
# discrete set of numbers
data1 = [1, 5, 6, 4, 4]
 
x = statistics.mean(data1)
 
# Mean
print("Mean is :", x)


  • Output : 
Mean is : 4
  • Trimmed Mean : Arithmetic Mean is influenced by the outliers (extreme values) in the data. So, trimmed mean in used at the time of pre-processing when we are handling such kinds of data in machine learning. 
    It is arithmetic having a variation i.e. it is calculated by dropping a fixed number of sorted values from each end of the sequence of data given and then calculated the mean (average) of remaining values. 
     

  • Example – 
     
Sequence = {0, 2, 1, 3}
p        = 0.25

Remaining Sequence  = {2, 1}
n, Total values = 2
Mean = 3/2 = 1.5
  • Code – 

Python3




# Trimmed Mean
 
from scipy import stats
 
# discrete set of numbers
data = [0, 2, 1, 3]
 
x = stats.trim_mean(data, 0.25)
 
# Mean
print("Trimmed Mean is :", x)


  • Output : 
Trimmed Mean is : 1.5
  • Weighted Mean : Arithmetic Mean or Trimmed mean is giving equal importance to all the parameters involved. But whenever we are working in machine learning predictions, there is a possibility that some parameter values hold more importance than the others, so we assign high weights to the values of such parameters. Also, there can be a chance that our data set has a highly variable value of a parameter, so we assign lesser weights to the values of such parameters. 
     

  • Example – 
Sequence = [0, 2, 1, 3]
Weight   = [1, 0, 1, 1]

Sum (Weight * sequence)  = 0*1 + 2*0 + 1*1 + 3*1
Sum (Weight) = 3
Weighted Mean = 4 / 3 = 1.3333333333333333
  • Code 1 – 

Python3




# Weighted Mean
 
import numpy as np
 
# discrete set of numbers
data = [0, 2, 1, 3]
 
x = np.average(data, weights =[1, 0, 1, 1])
 
# Mean
print("Weighted Mean is :", x)


  • Output 1 : 
Weighted Mean is : 1.3333333333333333
  • Code 2 – 

Python3




# Weighted Mean
 
data = [0, 2, 1, 3]
weights = [1, 0, 1, 1]
 
x = sum(data[i] * weights[i]
    for i in range(len(data))) / sum(weights)
 
 
print ("Weighted Mean is :", x)


  • Output 2 : 
Weighted Mean is : 1.3333333333333333


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