Geometric Mean Calculator

Enter all the numbers separated by comma (,)
Results:
Total Numbers:
Geometric Mean

Geometric Mean Calculator

Our Geometric Mean Calculator is designed for calculating the geometric mean of a set of numbers, useful in various fields like finance and science.

Understanding Geometric Mean

The geometric mean is a type of average used for data that varies exponentially or in a non-linear manner.

Uses of the Geometric Mean Calculator

  • Financial Analysis
  • Environmental Science
  • Educational Purposes

Who Uses This Calculator?

  • Economists and Financial Analysts
  • Environmental Scientists
  • Students and Educators
  • Quality Control Analysts

The Geometric Mean Calculation Formula

The formula for calculating the geometric mean is:

\[ \text{Geometric Mean} = \left( \prod_{i=1}^{n} a_i \right)^{\frac{1}{n}} \]

Frequently Asked Questions

How do you calculate the geometric mean?

Multiply all the numbers together and take the \( n \)-th root of the product, where \( n \) is the number of values.

What is the geometric mean of 5 and 10?

The geometric mean of 5 and 10 is \( \sqrt{5 \times 10} \), which equals approximately 7.07.

What is the geometric mean of 1, 2, 1/4, 1/5, 9/72, and 7/4?

Multiply all these numbers together and take the sixth root of the product.

What is the geometric mean of 7 and 12?

The geometric mean of 7 and 12 is \( \sqrt{7 \times 12} \).

What is the geometric mean of 1, 3, 5, 7, 9?

Multiply 1, 3, 5, 7, 9 and take the fifth root of the product.

What is the geometric mean of 5 numbers?

Multiply the five numbers together and take the fifth root of the product.

What is the geometric mean of 2, 6, 9, 5, 12?

Multiply 2, 6, 9, 5, 12 and take the fifth root of the product.

What is the formula of geometric mean in Class 10?

The formula is the \( n \)-th root of the product of \( n \) numbers.

What is the geometric mean of 3, 6, 24, and 48?

Calculate by multiplying 3, 6, 24, 48, and taking the fourth root.

Can geometric mean be negative?

No, the geometric mean cannot be negative as it involves multiplying numbers and extracting roots.

Why is geometric mean used?

It's used for data that involves ratios and requires averaging in a multiplicative manner.

What is the geometric mean of 9 and 16?

The geometric mean is \( \sqrt{9 \times 16} \), which equals 12.