Harmonic Mean Calculator

What is the Harmonic Mean?

The harmonic mean is a type of average that is calculated by dividing the number of values in a dataset by the sum of the reciprocals of all the values. It's particularly useful when working with rates or speeds.

Formula and Its Meaning

The formula for the harmonic mean (HM) is:

\[HM = \frac{n}{\sum_{i=1}^{n} \frac{1}{x_i}}\]

Where:

• \(n\) is the number of values in the dataset
• \(x_i\) represents each individual value in the dataset
• \(\sum\) denotes the sum of the terms

Calculation Steps

1. Take the reciprocal (1/x) of each number in your dataset.
2. Calculate the sum of these reciprocals.
3. Divide the count of numbers by this sum.

Example Calculation

Let's calculate the harmonic mean for the dataset: 2, 4, 8

1. Reciprocals: 1/2, 1/4, 1/8
2. Sum of reciprocals: 1/2 + 1/4 + 1/8 = 7/8
3. Harmonic Mean: 3 / (7/8) = 24/7 ≈ 3.43

Visual Representation

This scatter plot represents the example dataset (2, 4, 8). The red dashed line indicates the harmonic mean (approximately 3.43).