1. What is the Harmonic Mean?

The Harmonic Mean is a type of average, typically used for rates and ratios. 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:

• \( n_1 \) — First Number
• \( n_2 \) — Second Number
• \( n_3 \) — Third Number

Explanation: The harmonic mean is particularly useful when dealing with rates, speeds, or other quantities where the average of ratios is desired.

3. Importance of Harmonic Mean

Details: The harmonic mean provides the correct average for rates and ratios, making it essential in finance, physics, and engineering applications where average rates need to be calculated.

4. Using the Calculator

Tips: Enter three positive numbers. All values must be greater than zero as division by zero is undefined in the reciprocal calculation.

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, such as average speed over multiple trips with different distances.

Q2: What are the limitations of harmonic mean?
A: Harmonic mean cannot be calculated if any of the values are zero, as it involves taking reciprocals.

Q3: Can harmonic mean handle negative numbers?
A: No, harmonic mean is typically used with positive numbers only, as negative reciprocals can lead to misleading results.

Q4: How does harmonic mean compare to geometric mean?
A: Harmonic mean is always less than or equal to the geometric mean, which in turn is always less than or equal to the arithmetic mean.

Q5: What are practical applications of harmonic mean?
A: Common applications include calculating average speed, average fuel economy, and in finance for price-earnings ratios.