Understanding Types of Mean | Set 2

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

• Geometric Mean: Like arithmetic mean is the sum of all the discrete values in the set, Geometric mean is the product of discrete values in the set. It is useful for the set of positive discrete values. 
  

Example – 

Sequence = {1, 3, 9}

product         = 27
n, Total values = 3
Harmonic Mean   = (27)^(1/3)

Code – 

Python3

# Geometric Mean

import numpy as np

# discrete set of numbers
from scipy.stats.mstats import gmean
x = gmean([1, 3, 9])

# Mean
print("Geometric Mean is :", x)

Output : 

Geometric Mean is : 3

• Harmonic Mean : Harmonic mean plays it roles when it comes to calculate the mean of the terms which are in defined in relation to any unit. It is the reciprocal of the mean of the reciprocals of the data. It is used where inverse variation in relation is involved in the data. 
  

Example – 

Sequence = {1, 3, 9}

sum of reciprocals = 1/1 + 1/3 + 1/9
n, Total values    = 3
Harmonic Mean      = 3 / (sum of reciprocals)

Code – 

Python3

# Harmonic Mean

import numpy as np

# discrete set of numbers
from scipy.stats.mstats import hmean
x = hmean([1, 3, 9])

# Mean
print("Harmonic Mean is :", x)

Output : 

Harmonic Mean is : 2.076923076923077

• Relationship between Arithmetic (AM), Harmonic (HM) and Geometric Mean (GM):
  

Example – 

Sequence = {1, 3, 9}

sum of reciprocals = 1/1 + 1/3 + 1/9
Sum                = 10
Product            = 27
n, Total values    = 3

Arithmetic Mean = 4.33
Geometric Mean  = 3 
Harmonic Mean   = 3 / (sum of reciprocals) = 2.077