Geometric mean and harmonic mean

Indian Economy glossary

Also called: GM, HM · Topic: Economic Data: Census, NSS, Surveys and Statistical Tools · NCERT: Class 11, Ch 5 "Measures of Central Tendency"

Meaning

These are two special averages.

  • Geometric mean: GM = ⁿ√(x₁·x₂…xₙ), the n-th root of the product of n values. It suits growth rates and ratios, where changes build on each other. The compound annual growth rate is a geometric mean: CAGR = (end/start)^(1/n) − 1.
  • Harmonic mean: HM = n / Σ(1/x), the number of values divided by the sum of their reciprocals. It suits averaging rates such as speed.

Example

India's population grew 17.7% in the decade 2001-11. The yearly rate is 1.177^(1/10) − 1 ≈ 1.64% a year, not 17.7 ÷ 10 = 1.77%.

For speed: drive a fixed distance at 60 km/h and return at 40 km/h. The average speed is the HM, 2 ÷ (1/60 + 1/40) = 48 km/h, not 50 km/h.

Don't confuse with

  • Arithmetic mean: this simply adds values and divides by their number. For compounding growth or for rates, it overstates the true average.

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