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Table of Content
 1 What is a Geometric Mean? 2 What is Geometric Mean formula? 3 Geometric mean vs Arithmetic mean: 4 Finding the Geometric mean in terms of Logarithm: 5 Applications of Geometric Mean: 6 How to find geometric mean manually (Step-by-Step)? 7 How is geometric mean calculated? 8 What is the geometric mean of 4 and 9? 9 What is the geometric mean of 6 and 13? 10 Why is geometric mean better than arithmetic? 11 How do you know if something is arithmetic or geometric? 12 What is the relation between arithmetic mean and geometric mean? 13 Is geometric mean the same as median? 14 How do you find a common ratio in geometric mean? 15 How to find a geometric mean in excel?
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An online geometric mean calculator helps to calculate the geometric mean for a given data set of numbers or percentages. In other words, this geometric average calculator allows you to find the geometric average of the statistical set of numbers/percentages.

Now, give a thorough read to this important & helpful content to know about geometric mean formula, how to calculate it step-by-step and by using a calculator, and different related terms. First, we are going to start with the most basics!

## What is a Geometric Mean?

The number represents the central tendency by taking the nth root of the product of n numbers is referred to as the geometric mean. Also, it is known as geometric average is defined as “the product of n numbers raised to the power of 1/n”.In arithmetic mean, we add the total numbers then divided by the total numbers. In Geometric mean,we multiply the numbers then take its nth root.

Due to the formula of geometric mean, all the numbers of the data set must have the same sign, they must be all positive or all negative.

Also, try this online median mode range and mean calculator online to find the mean median mode and range for the given data set.

### What is Geometric Mean formula?

This online geometric mean calculator uses the following formula to find the GM, Where,

n is the total number of values

xi is the values of (x1, x2, x3, xn).

This geometric mean equation is equals to, The free average calculator by calculator-online allows you to find out the average or mean value for a given data set values. You can also try this best coefficient of variation calculator for dataset mean calculations as a coefficient of variance is referred to as the ratio of the standard deviation to the mean (average).

The coefficient of variance (CV) is the ratio of the standard deviation to the mean (average).

### Geometric mean for negative numbers:

As from the above formula and definition, we can see that we can only calculate the geometric mean for all the positive numbers or the numbers have to be the same sign. By taking the geometric mean of positive negative numbers results in an imaginary number. But this doesn’t mean we cannot find out the geometric mean of negative numbers.

Let’s say we have the changes of production in consecutive three years as 7% growth,9% decline,10%growth. The total growth after three years is 6.89%. But how do we calculate the yearly growth rate?

We can write all the values in proportions as,

7% growth = 1+7% = 1+7/100 = 1.07

9% decline = 1-9% = 1-9/100 = 0.91

10% growth = 1+10% = 1+10/100 = 1.1

Then, the GM = 1.0231

This geometric mean calculator works according to this scenario, so no need to do the manual transformation. You can enter the values with percentages like 2%, -8%,34% in this online tool.

## Geometric mean vs Arithmetic mean:

When we are dealing with two different ranges of values assuming they are equal one of small range like from 0-5 and the other is of large range from 900-1000, then this is the perfect case to use the geometric mean instead of arithmetic. The arithmetic mean neglects the small number.

When the data is skewed downwards and has the large positive outliers, then the geometric mean is handy in contrast with the arithmetic mean.

The mathematical relationship between arithmetic and geometric mean is:

Arithmetic mean ≥ Geometric mean

According to empirical rule calculations, symmetric distribution about the mean is said to be as the normal distribution, and remember that the data which is near the mean/average occur more frequently than the data far from mean/average.

### Finding the Geometric mean in terms of Logarithm:

You can also calculate the geometric mean by taking the logarithm of numbers of the data set.

The general formula in terms of logarithm is given below,

log(a*b*c)1/3 = 1/3 * log (a*b*c) = (1/3) * ((log a) + (log b) + (log c))

In simple words, you can find the geometric mean by:

• Take the logarithm of numbers.

• Calculate the arithmetic mean of the data.

• Then, taking the antilog of the result to find out the geometric mean.

An online geometric mean calculator can readily calculate the gemetric mean of the given statistical data such as number or percenages. This geometric average calculator will shows you the step-by-step calculations for the given set of numbers/percentages and find different mathematical related-terms.

### How to find Geometric mean with the calculator:

Finding geometric mean between numbers and percentages becomes very easy with this free online calculator. So, just follow the given steps to find the geometric mean of two numbers and percentages.

Inputs:

• First of all, select from the drop-menu how numbers are separated. It is either separated by comma, space or user defined. (If you select the “user define”, then enter the separation technique in the next field)
• Then, enter the numbers or percentages for which you want to perform calculations
• At the end, select the numbers type.
• Finally, hit the calculate button.

Outputs:

Once you fill all the fields of geometric average calculator, it will generate:

• Geometric mean of the data set.
• Complete step-by-step calculation.
• Arrange numbers in Ascending order.
• Arrange numbers in Descending order.
• Even numbers in the data.
• Odd numbers in the data.
• Total sum of the numbers.
• Maximum value.
• Minimum value.
• Total numbers.

## Applications of Geometric Mean:

Geometric means are used in different fields like in finance, social sciences geometry and in mathematics. InFinance, when you want to evaluate an offer for a deposit with the compound interest, or dealing with repayments, then you have to deal with geometric mean not arithmetic mean. In social sciences, when you need to say human population growth rate and it is expressed in the percentage, then geometric mean is helpful to answer. You can say that “the average growth rate of population of X city in Y years is Z”.

But, it frequently used in geometry. In the right-angled-triangle, perpendicular is the line extended perpendicularly from the hypotenuse to its vertex. If this line divides the hypotenuse in two parts, then the geometric mean of these length is equal to the length of perpendicular. Geometric means plays an important role in deciding the 16:9 aspects in modern tv screens and monitors.

Also, you can try the online harmonic mean calculator that helps you to calculate harmonic mean from the dataset, by dividing the sum of reciprocals of the dataset.

How to find geometric mean manually (Step-by-Step)?

The formula used for the geometric mean calculation between the numbers is as follow, This formula is equivalent to: Geometric mean example:

Find the geometric mean between 12,23,34?

Solution:

Step 1:

G.M = 3√ (12 × 23 × 34)

Step 2:

G.M = 3√ (9384)

Step 3:

G.M = 21.0926

### Manual example for the percentage numbers type:

Calculate the geometric between 11%,22%,33%?

Solution:

Step 1:

G.M = 3√ ((1+11/100) × (1+22/100) × (1+33/100) )

Step 2:

G.M = 3√ (1.11 × 1.22 × 1.33)

Step 3:

G.M = 3√ (1.8010)

Step 4:

G.M = 1.216

Step 5:

G.M = (1.216-1) × 100

Step 6:

G.M = 21.66%

You can give a try to our geometric mean calculator to verify this example problem.

### How is geometric mean calculated?

The geometric mean is calculated by multiplying the several numbers and takes the 1/nth power.

### What is the geometric mean of 4 and 9?

The geometric mean of 4 and 9 is 6.

By multiplying 9 and 4 results in 36, then taking the square root of 36 which gives the 6 as a geometric mean between 4 and 9.

### What is the geometric mean of 6 and 13?

8.83 is the geometric mean of the 6 and 13.

### Why is geometric mean better than arithmetic?

The geometric mean is better than arithmetic, because it also deals with the compounding from period to period. That’s why investors use geometric means rather than the arithmetic mean as it gives accurate measure of returns.

### How do you know if something is arithmetic or geometric?

An arithmetic sequence is a sequence having the same difference between the two consecutive terms while a geometric sequence has the constant ratio between the terms.

### What is the relation between arithmetic mean and geometric mean?

Let A.M and G.M are arithmetic and geometric between two positive numbers, then

A. M>G.M. Arithmetic mean can never be less than geometric mean.

### Is geometric mean the same as median?

Yes, geometric mean is the same as median because geometric mean involves the product of terms.

### How do you find a common ratio in geometric mean?

In geometric sequence,

• Divide each term by its previous term.
• Then compare the results if they are the same, then the sequence is geometric.

### How to find a geometric mean in excel?

To find geometric mean in excel, the following function is used:

=GEOMEAN (number1, [number2], ….)

Where,

number1 = The first value or cell reference.

number2 = The second value or cell reference of second value.

## End-Note:

The geometric mean is very helpful in many situations like calculating the growth rate of interest, determining compound interest, averages of area and volume, stock exchange market, and many others. So, you can use this online free geometric mean calculator will allow you to calculate the geometric mean between numbers or in percentage numbers with complete step-by-step calculation.

## References:

From the source of Wikipedia: Geometric mean and Calculation, Relationship with logarithms, and much more!

From the source of investopedia: Breaking Down the Geometric Mean in Investing

From the source of themodelmill: Geometric Mean and Standard Deviation (used for investments that have a maturity horizon)