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Statistical function

HARMEAN

Returns the harmonic mean.

Rarely usedDifficulty 1300 · ProficientUsage rank #304 of 520
Practice · 2 questions →

When to use it

The harmonic mean: n divided by the sum of reciprocals. The correct average for rates measured per unit, like speeds over equal distances or price-to-earnings ratios.

The shape of it

Syntax
=HARMEAN(number1, [number2], ...)

Worked examples

  • Two numbers

    =HARMEAN(2,8) → 3.2

    Two divided by (1/2 + 1/8).

  • Average speed

    =HARMEAN(60,40) → 48

    Average speed for a trip out at 60 and back at 40 over the same distance; not 50.

  • Average ratio

    =HARMEAN(A2:A6) → 14.2

    Average P/E ratio of five holdings with equal weights.

Worth knowing

  • Always the smallest of the three means: harmonic ≤ geometric ≤ arithmetic.
  • Use when the quantity in the denominator is what is being held equal.
  • Weighted harmonic mean needs SUMPRODUCT: SUM(w)/SUMPRODUCT(w,1/x).

Where it goes wrong

  • #NUM! for zero or negative values.
  • Blanks and text are ignored.

Related

AVERAGECOUNTCOUNTACOUNTIFCOUNTIFSMAX

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