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






 
' FB 1.05.0 Win64
 
Function ArithmeticMean(array() As Double) As Double
  Dim length As Integer = Ubound(array) - Lbound(array) + 1
  Dim As Double sum = 0.0
  For i As Integer = LBound(array) To UBound(array)
    sum += array(i)
  Next
  Return sum/length
End Function
 
Function GeometricMean(array() As Double) As Double
  Dim length As Integer = Ubound(array) - Lbound(array) + 1
  Dim As Double product = 1.0
  For i As Integer = LBound(array) To UBound(array)
    product *= array(i)
  Next
  Return product ^ (1.0 / length) 
End Function
 
Function HarmonicMean(array() As Double) As Double
  Dim length As Integer = Ubound(array) - Lbound(array) + 1
  Dim As Double sum = 0.0
  For i As Integer = LBound(array) To UBound(array)
    sum += 1.0 / array(i)
  Next
  Return length / sum
End Function
 
Dim vector(1 To 10) As Double
For i As Integer = 1 To 10
  vector(i) = i
Next
 
Print "Arithmetic mean is :"; ArithmeticMean(vector())
Print "Geometric mean is  :"; GeometricMean(vector())
Print "Harmonic mean is   :"; HarmonicMean(vector())
Print
Print "Press any key to quit the program"
Sleep
 