Geometric Mean Examples
Example 1: Calculate the geometric mean of the sequence, 2, 4, 6, 8, 10, 12.
Solution:
Given,
- Sequence, 2, 4, 6, 8, 10, 12
Product of terms (P) = 2 Γ 4 Γ 6 Γ 8 Γ 10 Γ 12 = 46080
Number of terms (n) = 6
Using the formula,
GM = (P)1/n
GM = (46080)1/6
GM = 5.98
Example 2: Calculate the geometric mean of the sequence, 4, 8, 12, 16, 20.
Solution:
Given,
- Sequence, 4, 8, 12, 16, 20
Product of terms (P) = 4 Γ 8 Γ 12 Γ 16 Γ 20 = 122880
Number of terms (n) = 5
Using the formula,
GM = (P)1/n
GM = (122880)1/5
GM = 10.42
Example 3: Calculate the geometric mean of the sequence, 5, 10, 15, 20.
Solution:
Given,
- Sequence, 5, 10, 15, 20
Product of terms (P) = 5 Γ 10 Γ 15 Γ 20 = 15000
Number of terms (n) = 4
Using the formula,
GM = (P)1/n
GM = (15000)1/4
GM = 11.06
Example 4: Find the number of terms in a sequence if the geometric mean is 32 and the product of terms is 1024.
Solution:
Given,
- Product of terms (P) = 1024
- GM of terms = 32
Using the formula,
GM = (P)1/n
β 1/n = log GM/log P
β n = log P/log GM
β n = log 1024/log 32
β n = 10/5
β n = 2
Example 5: Find the number of terms in a sequence if the geometric mean is 8 and the product of terms is 4096.
Solution:
Given,
- Product of terms (P) = 4096
- GM of terms = 8
Using the formula,
GM = (P)1/n
β 1/n = log GM/log P
β n = log P/log GM
β n = log 4096/log 8
β n = 12/3
β n = 4
Example 6: Find the number of terms in a sequence if the geometric mean is 4 and the product of terms is 65536.
Solution:
Given,
- Product of terms (P) = 65536
- GM of terms = 4
Using the formula,
GM = (P)1/n
β 1/n = log GM/log P
β n = log P/log GM
β n = log 65536/log 4
β n = 16/2
β n = 8
Example 7: Find the number of terms in a sequence if the geometric mean is 16 and the product of terms is 16777216.
Solution:
Given,
- Product of terms (P) = 16777216
- GM of terms = 16
Using the formula we have,
GM = (P)1/n
β 1/n = log GM/log P
β n = log P/log GM
β n = log 16777216/log 16
β n = 24/4
β n = 6
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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