Comprehensive Calculator Guide
This calculator finds the harmonic mean of positive numbers, the count divided by the sum of the reciprocals, and compares it with the arithmetic and geometric means. It is the right average for rates: out at 40 km/h and back the same way at 60 km/h averages 48 km/h, not 50.
Harmonic mean
For two values it is 2ab ÷ (a + b). Use it for rates over equal amounts: speeds over equal distances, prices when spending the same each time. Always harmonic ≤ geometric ≤ arithmetic.
How to Use
- Enter positive numbers separated by commas or spaces.
- For speeds, use equal-distance legs.
- Press “Calculate” to see the harmonic mean.
Formula Used
n ÷ (1/x₁ + … + 1/xₙ)
Practical Examples
- Example 1
- 40 and 60: 48.
- Example 2
- 2, 3, 6: 3.
Important Tips
- Equal distances: harmonic; equal times: arithmetic.
- Two values: 2ab/(a + b).
- It should be below the arithmetic mean.
Common Mistakes to Avoid
- Averaging speeds arithmetically.
- Using it for equal times.
- Including a zero.
Frequently Asked Questions
- 60 out, 90 back?
- 72 km/h.
- Why lower?
- Small values weigh more.
- When is arithmetic right?
- Equal time at each speed.