The harmonic mean
(1)
The harmonic mean of a list of numbers may be computed in the Wolfram
Language using HarmonicMean list ].
The special cases of
and so on.
The harmonic means of the integers from 1 to A102928 and A001008 ).
For arithmetic mean geometric
mean
(4)
(Havil 2003, p. 120).
The harmonic mean is the special case power mean and is
one of the Pythagorean means . In older literature,
it is sometimes called the subcontrary mean.
The volume -to-surface area ratio for a cylindrical container with height mean curvature of
a general surface are related to the harmonic mean.
Hoehn and Niven (1985) show that
(5)
for any positive constant
See also Arithmetic Mean ,
Arithmetic-Geometric Mean ,
Geometric Mean ,
Harmonic-Geometric
Mean ,
Harmonic Range ,
Power
Mean ,
Pythagorean Means ,
Root-Mean-Square
Explore with Wolfram|Alpha
References Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. Havil, J. Gamma:
Exploring Euler's Constant. Hoehn, L. and Niven, I. "Averages on the Move." Math.
Mag. 58 , 151-156, 1985. Kenney, J. F. and Keeping, E. S.
"Harmonic Mean." §4.13 in Mathematics
of Statistics, Pt. 1, 3rd ed. Sloane, N. J. A. Sequences A001008 /M2885
and A102928 in "The On-Line Encyclopedia
of Integer Sequences." Zwillinger, D. (Ed.). CRC
Standard Mathematical Tables and Formulae. Referenced on Wolfram|Alpha Harmonic Mean
Cite this as:
Weisstein, Eric W. "Harmonic Mean." From
MathWorld https://mathworld.wolfram.com/HarmonicMean.html
Subject classifications
of 
numbers 
(where 
, ..., 
) is the number 
defined by
and 
are therefore given by
for 
, 2, ... are 1, 4/3, 18/11, 48/25, 300/137, 120/49, 980/363,
... (OEIS A102928 and A001008).
,
the harmonic mean is related to the arithmetic mean 
and geometric
mean 
by
of the power mean and is
one of the Pythagorean means. In older literature,
it is sometimes called the subcontrary mean.
and radius 
and the mean curvature of
a general surface are related to the harmonic mean.
.
