1. What is Harmonic Mean?

The harmonic mean is a type of average that is appropriate for situations when the average of rates is desired. It is calculated by dividing the number of observations by the sum of the reciprocals of each observation.

2. How Does the Calculator Work?

The calculator uses the harmonic mean formula:

Where:

• \( n \) — Number of values
• \( x_i \) — Each individual value

Explanation: The harmonic mean is particularly useful when dealing with rates, ratios, or situations where the average of reciprocals is meaningful.

3. When to Use Harmonic Mean

Details: The harmonic mean is commonly used in finance (average price-to-earnings ratios), physics (average speeds), and other fields where rates are important.

4. Using the Calculator

Tips: Enter numeric values separated by commas. All values must be non-zero. The calculator will ignore any non-numeric values.

5. Frequently Asked Questions (FAQ)

Q1: When should I use harmonic mean instead of arithmetic mean?
A: Use harmonic mean when averaging rates or ratios, especially when the rates are defined per unit of time or per unit of some other quantity.

Q2: What's the difference between harmonic, geometric, and arithmetic means?
A: For any dataset, harmonic mean ≤ geometric mean ≤ arithmetic mean. Each is appropriate for different types of data.

Q3: Can harmonic mean be used with negative numbers?
A: No, harmonic mean is undefined for negative numbers and zero.

Q4: What's a practical example of harmonic mean use?
A: Calculating average speed when traveling equal distances at different speeds (e.g., 60 mph one way and 40 mph return trip).

Q5: Why is it called "harmonic" mean?
A: The term comes from its relationship to the harmonic series in music and mathematics.