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Geometric & Harmonic Mean

Math Calculators

AM-GM-HM inequality, growth rates

Quick Answer

Geometric & Harmonic Mean: AM-GM-HM inequality, growth rates. Geometric & Harmonic Mean uses standard math formulas to compute accurate results instantly.

Geometric mean
4
Harmonic mean
3.2
Arithmetic mean5
RMS 均方根5.8309519
n2
GM² = AM × HM16

Mean inequality chain

HM3.2≤GM4≤AM5≤RMS5.8309519

Calculation steps

  1. 1n = 2; product = 16
  2. 2GM = (product)^(1/n) = 16^(1/2) = 4
  3. 3HM = n / Σ(1/xᵢ) = 2 / 0.625 = 3.2
  4. 4AM = Σxᵢ / n = 10 / 2 = 5

Which mean when?

MeanUse case
Arithmetic AMAdditive quantities: scores, heights, incomes
Geometric GMGrowth rates, investment CAGR, aspect ratios
Harmonic HMAverage speed over equal distances, P/E ratios, parallel resistors
RMSAC voltage, standard deviation, signal power
💡 Classic trap: driving 60 km/h out and 40 km/h back over the SAME distance gives average speed = HM = 48 km/h, NOT 50. Reason: you spend more time at the slower speed. Over equal TIMES the AM would be right.

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Formula & How It Works

Geometric & Harmonic Mean formula

Geometric & Harmonic Mean uses standard math formulas to compute accurate results instantly.

FAQ

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Source & Updates

Standard mathematical formulas. All logic verified. Last updated: 2025-07

Last updated:

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