Practice Questions on Geometric Mean

Q1. Calculate the geometric mean of the sequence, 15, 25, 35, 45.

Q2. What is the geometric mean of 7 and 28?

Q3. Find the number of terms in a sequence if the geometric mean is 22 and the product of terms is 655360.

Q4. What is the geometric mean of 4 and 25?

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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What is Geometric Mean?

Geometric Mean (GM) is the nth root of the product of the given dataset. It gives the central measure of the data set. To find the geometric mean of various numbers we first multiply the given numbers and then take the nth root of the given number. Suppose we are given 3 numbers 3, 9, and 27 then the geometric mean of the given values is calculated by taking the third root of the product of the three given data. The calculation of Geometric Mean is shown below:...

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,...

Geometric Mean of Two Numbers

Suppose we are given two numbers ‘a’ and ‘b’ then the geometric mean of the two numbers is calculated as,...

Difference Between Arithmetic Mean and Geometric Mean

The difference between Arithmetic Mean and the Geometric Mean is explained in the table below,...

How to Find the Geometric Mean?

The geometric mean of two numbers is found using the formula, GM = √(ab), where a and b are the two numbers....

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,...

Geometric Mean Properties

Various properties of the geometric mean are,...

Geometric Mean Theorem

Geometric mean theorem states that, if h is the altitude of the right angle triangle and a and b are the two segments of the hypotenuse then,...

Application of Geometric Mean

Geometric mean is the measure of the central tendency that is highly used in mathematics and related fields. Some applications of the Geometric mean are,...

Geometric Mean Examples

Example 1: Calculate the geometric mean of the sequence, 2, 4, 6, 8, 10, 12....

Practice Questions on Geometric Mean

Q1. Calculate the geometric mean of the sequence, 15, 25, 35, 45....

Geometric Mean – FAQs

What is Geometric Mean?...

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