Calculation: The Harmonic Mean Calculator is a tool used to calculate the harmonic mean, a type of average that is particularly useful in fields like physics, finance, and statistics, where rates or ratios are involved.
What is the Harmonic Mean Calculator?
The Harmonic Mean Calculator is used to compute the harmonic mean of a set of numbers, which provides a better average in situations where smaller numbers have a larger impact on the overall average, such as in calculating rates or speeds.
Harmonic Mean Calculator Formula
The harmonic mean is the arithmetic mean of the reciprocals of the numbers. It is calculated using the following formula:
Harmonic Mean = n / ( (1/x₁) + (1/x₂) + ... + (1/xₙ) )Where:
- n represents the total number of values.
- x₁, x₂, …, xₙ represent the actual numbers whose average is being calculated.
Harmonic Mean Calculator examples?
Example 1:
Consider a vehicle with speeds of 60 km/h, 80 km/h, and 100 km/h. We want to calculate the harmonic mean of the average speed of the vehicle.
Steps:
- n = 3 (Since there are 3 speed values)
- Numbers: x₁ = 60, x₂ = 80, x₃ = 100
- Apply the formula:
Harmonic Mean = 3 / ( (1/60) + (1/80) + (1/100) )
Harmonic Mean = 3 / (0.0167 + 0.0125 + 0.0100)
Harmonic Mean = 3 / 0.0392
Harmonic Mean ≈ 76.5 km/h
Result: The harmonic mean speed of the vehicle is approximately 76.5 km/h.
Example 2:
An investor has received returns of 10%, 15%, and 20% over three years. We want to calculate the average annual return using the harmonic mean.
Steps:
- n = 3 (Since there are 3 years)
- Numbers: x₁ = 10, x₂ = 15, x₃ = 20
- Apply the formula:
Harmonic Mean = 3 / ( (1/10) + (1/15) + (1/20) )
Harmonic Mean = 3 / (0.1 + 0.0667 + 0.05)
Harmonic Mean = 3 / 0.2167
Harmonic Mean ≈ 13.85%
Result: The investor’s average annual return is approximately 13.85%.
Using the Harmonic Mean Calculator enables more accurate analysis of ratios and allows for healthier calculations in various fields.