1. What is Weighted Harmonic Mean?

The weighted harmonic mean is a type of average that is appropriate when averaging rates or ratios where different weights are assigned to different elements. It gives more importance to smaller values compared to the arithmetic mean.

2. How Does the Calculator Work?

The calculator uses the weighted harmonic mean formula:

Where:

• \( w_i \) — Weight of the i-th element
• \( x_i \) — Value of the i-th element
• \( n \) — Number of elements

Explanation: The formula calculates the reciprocal of the weighted average of the reciprocals of the values.

3. Applications of Weighted Harmonic Mean

Details: Commonly used in finance (e.g., price-earnings ratios), physics (average speeds), and other fields where rates need to be averaged with different weights.

4. Using the Calculator

Tips: Enter comma-separated values and their corresponding weights. Both lists must have the same number of elements. Values and weights must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: When should I use weighted harmonic mean instead of arithmetic mean?
A: Use WHM when averaging rates or ratios, especially when different elements have different importance (weights).

Q2: What happens if one of the values is zero?
A: The calculator automatically excludes zero values since division by zero is undefined.

Q3: Can weights be negative?
A: No, weights must be positive numbers. Negative weights would make the result meaningless.

Q4: How does this differ from regular harmonic mean?
A: Regular harmonic mean assigns equal weights to all values, while weighted harmonic mean allows different weights.

Q5: What's a practical example of using WHM?
A: Calculating average speed when different parts of a journey are traveled at different speeds for different distances (weights).