Harmonic Mean Calculator

Harmonic Mean Formula:

\[ HM = \frac{n}{\sum_{i=1}^{n} \frac{1}{x_i}} \]

Harmonic Mean:

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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 the numbers in the series.

2. How Does the Calculator Work?

The calculator uses the harmonic mean formula:

\[ HM = \frac{n}{\sum_{i=1}^{n} \frac{1}{x_i}} \]

Where:

\( n \) — Number of elements
\( x_i \) — Each individual value in the set

Explanation: The harmonic mean gives less weight to large values and more weight to small values, making it useful for rates and ratios.

3. When to Use Harmonic Mean

Details: The harmonic mean is particularly useful when dealing with rates, ratios, or situations where you need to find an average of multiplicative factors.

4. Using the Calculator

Tips: Enter numbers separated by commas. All values must be numeric and 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 (like speed) or ratios where the denominator varies.

Q2: What are common applications of harmonic mean?
A: Finance (P/E ratios), physics (average speed), and computer science (load balancing).

Q3: Why can't any values be zero?
A: Because the harmonic mean involves reciprocals, and division by zero is undefined.

Q4: How does harmonic mean compare to other averages?
A: For any set of positive numbers: harmonic mean ≤ geometric mean ≤ arithmetic mean.

Q5: Can harmonic mean handle negative numbers?
A: No, harmonic mean is only defined for positive real numbers.