Introduction to the Geometric Mean Calculator
A geometric mean calculator is an online tool that is used to find the average value from a given set of numbers. It computes the given number in which it takes the product of all numbers and then square roots them to get the central tendency value in a couple of minutes.
You can use our geometric average calculator for mean value problems and get the solution without consuming your time in doing complex calculations manually.
What is the Geometric Mean?
The geometric mean is the average value that indicates the central tendency which comes from a set of numbers that multiply from the nth root to n numbers. It is a statistical method that describes the whole of about given number set.
Geometric mean has real-life applications as well like finding the annual growth and investment, in a stock exchange or financial growth rate. It is a commonly used application in biology to determine the growth of cell division or bacteria and its results after experiments.
Geometric Mean Formula
The geometric mean formula is mathematically written in square root form or with a square in an exponential form where its power is 1/n. The formula used by the geometric mean calculator with steps to solve such problems is,
$$ \biggr( \prod_{i = 1}^{n} X_i \biggr)^{\frac{1}{n}} \;=\; \sqrt[n]{x_1 x_2 … x_n} $$
Whereas,
n Total number of elements in a set
xn total element in a set
1/n is the exponential power of a number set
How to Find the Geometric Mean by Using Geomean Calculator
Geometric mean gives the mean value of a number set with the help of the geometric mean formula and Its solution gives you an idea about the growth rate of a given set. To find the geometric mean you should use the geometric mean calculator and follow some simple steps to get the right result for your question.
Step 1:
Identify the total number of elements n and total elements value x from the given number set
Step 2:
Apply the geometric mean formula and add all the values in it
Step 3:
Take the product of all these elements values as x1*x2*x3…..xn.
Step 4:
Take the square root of the result that gets after multiplication and the square root power is 1/n.
Step 5:
After taking the square root you will get the solution of the average value of a given set number.
Solved Example of Geometric Mean
The geometric means calculator can solve the geometric mean problems easily but it is important to understand the manual calculation. So, an example is given below,
Example:
Find the geometric mean of the numbers 4, 9, and 16.
Solution:
apply the geometric mean formula on the given set of number
$$ Geometric\; Mean \;=\; \sqrt{x^1 \times x^2 \times … \times x^n} $$
Here n=3 and x=4*9*16
$$ 4 \times 9 \times 16 \;=\; 576 $$
$$ Geometric\; Mean \;=\; \sqrt[3]{576} $$
$$ Geometric\; Mean \;=\; \sqrt[3]{576} \approx 8 $$
The geometric mean of a given set of numbers is approximately 8. To find the geometric mean of 14 and 20 you can use geomean calculator and would follow similar steps.
How to Calculate Geometric Mean on Geometric Average Calculator
Geometric mean calculator with steps provides you with the easiest method to solve mean values from a particular number set of problems. Follow some of our guidelines so that you can use our geomean calculator correctly for the evaluation. These steps are:
- Enter all the values of elements in the input box
- Enter the value of the total number of elements n in the second input box
- Click on the “Calculate” button to get the solution of the geometric mean problem from our calculator
- The Recalculate button will bring you back to the home page where you can evaluate more examples of geometric mean problem
- If you want to check the accuracy of our geometric means calculator then you use load example solution so that you get an idea about its precise solution
Outcome of the Geometric Mean Calculator with Steps
The geometric average calculator gives a solution of the average value that describes the number set immediately when you click on the calculate button. It may include as:
Result section
When you click on the result button it provides you with solutions of mean value problems
Possible Steps section
It provides you with solutions of geometric mean problems in step by step process.
Useful Features for Using Geometric Means Calculator
The geometric mean calculator provides you with multiple benefits whenever you use it to calculate mean value problems and give a solution. These benefits are:
- The geometric average calculator is a free tool so you can use it to find the geometric mean value problems in real time.
- It is a versatile tool that allows you to get the solution of various types of geometric mean problems
- You can try out our geomean calculator for practice with more examples so that you get a strong hold on the geometric average mean problem concept
- Our tool saves you time and effort from doing average value calculations without taking much time.
- It is a trustworthy tool that provides you with accurate solutions every time whenever you use it to calculate the geometric mean examples.
- It provides the solution with a complete process in a step-by-step method so that you get a better understanding on the geometric mean concept.
