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.

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

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

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

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

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

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