Relation Between AM, GM and HM
There is relation between (arithmetic mean) AM, (geometric mean) GM and (harmonic mean) HM that is used to find any one value if other two values are given. Suppose we are given two numbers ‘a’ and ‘b’ then AM, GM and HM is calculated as,
AM = (a+b)/2…(i)
GM = √(ab)…(ii)
HM = 2ab/(a+b)…(iii)
from (i), (ii) and (iii)
HM = GM2/AM
GM2 = AM × HM
This is the required AM, GM and HM inequalities.
Geometric Mean Formula
Geometric Mean is the measure of the central tendency used to find the central value of the data set in statistics. There are various types of mean that are used in mathematics including Arithmetic Mean(AM), Geometric Mean(GM), and Harmonic Mean(HM). In geometric mean, we first multiply the given number altogether and then take the nth root of the given product.
In this article, we will learn about Geometric Mean Definition, Geometric Mean Formula, Examples, and others in detail.
Table of Content
- What is Geometric Mean?
- Geometric Mean Definition
- Geometric Mean Formula
- Geometric Mean Formula Derivation
- Geometric Mean of Two Numbers
- Arithmetic Mean Vs Geometric Mean
- How to Find the Geometric Mean
- Relation Between AM, GM and HM
- Geometric Mean Properties
- Geometric Mean Theorem
- Application of Geometric Mean
- Geometric Mean Examples
- Practice Questions on Geometric Mean
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