HarmonicMean

Computes the harmonic mean of all elements in a container or in a sequence. The elements must be numbers.

Syntax

• HarmonicMean(X)

  • X is a vector, matrix, list, or set

• HarmonicMean(expr, var, a, b)

  • expr is an expression in one variable var

  • var is the variable in expr

  • a is the lower bound

  • b is the upper bound

Description

Computing the mean of a container

If X is a non-empty container of numbers, then HarmonicMean(X) is the harmonic mean of all elements in X.

The following container types are supported:

• vectors

  • the result is the mean of all components

• matrices

  • the result is the mean of all entries

• lists containing numbers

  • the result is the mean of all numbers

• sets containing numbers

  • the result is the mean of all numbers

Typewise, the elements may be either real or complex, and the result is complex iff at least one of the elements is complex.

Computing the mean of a sequence

HarmonicMean(expr, var, a, b) computes the harmonic mean of the expression expr in one variable var as var takes all integer values from a to b (inclusively).

expr must return a number.

Examples

Computing the mean of a container

HarmonicMean(❨5, 1, 2, 6, 3, 8, 4, 10, 2, 3❩)

2.85035629454	(=1200/421)

Computing the mean of a sequence

HarmonicMean(n^2 + 3⋅n + 1, n, 1, 100)

186.411917683

See also

• mean, average, ArithmeticMean

• GeometricMean