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 number in the series.

2. How Does the Calculator Work?

The calculator uses the harmonic mean formula:

Where:

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

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 numbers separated by commas. All values must be numeric and non-zero. The calculator will show both the result and step-by-step calculations.

5. Frequently Asked Questions (FAQ)

Q1: Why use harmonic mean instead of arithmetic mean?
A: Harmonic mean gives less weight to large outliers and more weight to small values, making it better for rates and ratios.

Q2: What's the difference between HM, AM, and GM?
A: For any dataset with positive numbers: HM ≤ GM ≤ AM. The equality holds only when all numbers are equal.

Q3: Can harmonic mean be used with zero values?
A: No, harmonic mean cannot be calculated if any value is zero (division by zero error).

Q4: What are practical applications of harmonic mean?
A: Calculating average speed, average fuel economy, P/E ratios in finance, and parallel resistance in electronics.

Q5: How does harmonic mean handle negative numbers?
A: Harmonic mean is typically only used with positive numbers. Negative values can produce misleading results.