Statistics Calculator: Pythagorean Means

Calculate the values of the three pythagorean means.

Data is from: Population Sample

Pythagorean Means Calculator

This page aggregates the calculations of the three means known as pythagorean means:

Type or paste the numbers in the box, using commas, spaces or new lines as separators. Press 'Submit Data' to make the calculation. Use only positive values or the geometric and harmonic means will not calculated. There is no need to choose whether tha data is from a population or a sample.

What are the pythagorean means

The pythagorean means, also known as the three "classic" means, are the arithmetic mean (A), the geometric mean (G) and the harmonic mean (H).

The harmonic mean of a group of numbers that are not all the same, is always smaller than the geometric mean, which is always smaller than the arithmetic mean. If the numbers in the group are all the same, the three means will be the same.

$ H \leq G \leq A $

For a more in-depth explanation, see this Wikipedia article.

Pythagorean means formulas

The following formulas are used to calculate the pythagorean means:

$ H = \frac{n}{\sum_{i=1}^n \frac{1}{x_i}} $                $ G = \left( \prod_{i=1}^n x_i \right)^\frac{1}{n} $                $ A ={\frac{1}{n} \sum_{i=1}^n (x_i) $