Geometric Mean Formula
The formula used to calculate the geometric mean of the given values is added below. Suppose we are given ‘n’ numbers x1, x2, x3, …, xn then its geometric mean is calculated using the formula,
The other formula used to find the geometric mean is,
GM = Antilog (∑ log xk)/n
where,
- ∑log xk is Logarithm Value of sum of all Values in a Sequence
- n is the Number of values in the Sequence
Geometric Mean Formula Derivation
Suppose x1, x2, x3, x4, ……, xn are the values of a sequence whose geometric mean has to be evaluated.
So, the geometric mean of the given sequence can be written as,
GM = √(x1 × x2 × x3 × … × xn)
GM = (x1 × x2 × x3 × … × xn)1/n
Taking log on both sides of the equation we get,
log GM = log (x1 × x2 × x3 × … × xn)1/n
Using, log formula log ab = b log a,
log GM = (1/n) log (x1 × x2 × x3 × … × xn)
Using property, log (ab) = log a + log b,
log GM = (1/n) (log x1 + log x2 + log x3 + … + log xn)
log GM = (∑ log xk)/n
Taking antilog on both sides we get,
GM = Antilog (∑ log xk)/n
This derives the formula for geometric mean of a series.
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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