Task[edit]
Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive).

Show that 



A
(

x

1


,
…
,

x

n


)
≥
G
(

x

1


,
…
,

x

n


)
≥
H
(

x

1


,
…
,

x

n


)


{\displaystyle A(x_{1},\ldots ,x_{n})\geq G(x_{1},\ldots ,x_{n})\geq H(x_{1},\ldots ,x_{n})}

 for this set of positive integers.

 The most common of the three means, the arithmetic mean, is the sum of the list divided by its length:
 



A
(

x

1


,
…
,

x

n


)
=




x

1


+
⋯
+

x

n



n




{\displaystyle A(x_{1},\ldots ,x_{n})={\frac {x_{1}+\cdots +x_{n}}{n}}}


 The geometric mean is the 



n


{\displaystyle n}

th root of the product of the list:
 



G
(

x

1


,
…
,

x

n


)
=




x

1


⋯

x

n




n





{\displaystyle G(x_{1},\ldots ,x_{n})={\sqrt[{n}]{x_{1}\cdots x_{n}}}}


 The harmonic mean is 



n


{\displaystyle n}

 divided by the sum of the reciprocal of each item in the list:
 



H
(

x

1


,
…
,

x

n


)
=


n



1

x

1




+
⋯
+


1

x

n









{\displaystyle H(x_{1},\ldots ,x_{n})={\frac {n}{{\frac {1}{x_{1}}}+\cdots +{\frac {1}{x_{n}}}}}}




See also
Tasks for calculating statistical measures



in one go
moving (sliding window)
moving (cumulative)

Mean
Arithmetic

Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means


Averages/Simple moving average




Geometric

Averages/Pythagorean means




Harmonic

Averages/Pythagorean means




Quadratic

Averages/Root mean square




Circular

Averages/Mean angle
Averages/Mean time of day




Median

Averages/Median




Mode

Averages/Mode




Standard deviation

Statistics/Basic



Cumulative standard deviation






a = .array~of(1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0)
say "Arithmetic =" arithmeticMean(a)", Geometric =" geometricMean(a)", Harmonic =" harmonicMean(a)
 
::routine arithmeticMean
  use arg numbers
  -- somewhat arbitrary return for ooRexx
  if numbers~isEmpty then return "NaN"
 
  mean = 0
  loop number over numbers
      mean += number
  end
  return mean / numbers~items
 
::routine geometricMean
  use arg numbers
  -- somewhat arbitrary return for ooRexx
  if numbers~isEmpty then return "NaN"
 
  mean = 1
  loop number over numbers
      mean *= number
  end
 
  return rxcalcPower(mean, 1 / numbers~items)
 
::routine harmonicMean
  use arg numbers
  -- somewhat arbitrary return for ooRexx
  if numbers~isEmpty then return "NaN"
 
  mean = 0
  loop number over numbers
      if number = 0 then return "Nan"
      mean += 1 / number
  end
 
  -- problem here....
  return numbers~items / mean
 
::requires rxmath LIBRARY