Understanding Types of Means | Set 1

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

• Arithmetic Mean: It is the mathematical expectation of a discrete set of numbers or averages. 
  Denoted by X̂, 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, ….. x_n
  

• 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 is 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 calculating the mean (average) of the 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 on machine learning predictions, there is a possibility that some parameter values hold more importance than 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