# Harmonic Mean

#### What is the Harmonic Mean?

In mathematics, the harmonic mean is an average measure that is also one of the three Pythagorean means. Its main application is in finding the average of rates.

Mathematically, the harmonic mean is usually denoted as H and can be expressed as:

Where x_{1}, x_{2}, … ,x_{n} is a set of n positive real numbers.

For data sets containing positive real numbers and at least one pair of non-equal values, the arithmetic mean gives the highest average, the harmonic mean the lowest value, and the geometric mean is placed in between these two numbers.

#### Why is the Harmonic Mean Important?

The harmonic mean is commonly applied in sciences and engineering. In Physics, it is used to calculate the speed of a mobile object moving between one point and another, and returning to the origin. In electricity, it is used to calculate the total resistance of several parallel resistors, and a similar principle applies to capacitors in parallel. In optics, it can be found in the thin lenses law and, in hydrology, in the average electric conductivity of a flow perpendicular to layers.

Likewise, in finance, it is used to calculate ratio averages, such as the price-earnings ratio. And, in machine learning, the harmonic mean is often used in the F-score as a performance metric for the evaluation of algorithms.

#### Harmonic Mean + LogicPlum

Although easy to calculate, knowing when to employ the harmonic mean requires specific knowledge in the area under study. This is particularly true when it is used to evaluate algorithmic performance.

The solution for this difficulty is automating the calculation process to minimize or even eliminate human intervention. LogicPlum’s platform follows this approach, helping its users to create models based on the latest machine learning technologies.

#### Guide to Further Reading

Cantrell, David W. “Pythagorean Means.” From MathWorld–A Wolfram Web Resource, created by Eric W. Weisstein. Available at https://mathworld.wolfram.com/PythagoreanMeans.html