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This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues.

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Compute all three of the [[wp:Pythagorean means|Pythagorean means]] of the set of integers 1 through 10 (inclusive).

Show that $A\left(x_1,\ldots,x_n\right) \geq G\left(x_1,\ldots,x_n\right) \geq H\left(x_1,\ldots,x_n\right)$ for this set of positive integers.

• The most common of the three means, the [[Averages/Arithmetic mean|arithmetic mean]], is the sum of the list divided by its length: : $A\left(x_1, \ldots, x_n\right) = \frac\left\{x_1 + \cdots + x_n\right\}\left\{n\right\}$

• The [[wp:Geometric mean|geometric mean]] is the $n$th root of the product of the list: : $G\left(x_1, \ldots, x_n\right) = \sqrt\left[n\right]\left\{x_1 \cdots x_n\right\}$

• The [[wp:Harmonic mean|harmonic mean]] is $n$ divided by the sum of the reciprocal of each item in the list: : $H\left(x_1, \ldots, x_n\right) = \frac\left\{n\right\}\left\{\frac\left\{1\right\}\left\{x_1\right\} + \cdots + \frac\left\{1\right\}\left\{x_n\right\}\right\}$

## 11l

F amean(num)
R sum(num)/Float(num.len)

F gmean(num)
R product(num) ^ (1.0/num.len)

F hmean(num)
return num.len / sum(num.map(n -> 1.0/n))

V numbers = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
print(amean(numbers))
print(gmean(numbers))
print(hmean(numbers))


{{out}}


5.5
4.52873
3.41417



## ActionScript

function arithmeticMean(v:Vector.<Number>):Number
{
var sum:Number = 0;
for(var i: uint = 0; i < v.length; i++)
sum += v[i];
return sum/v.length;
}
function geometricMean(v:Vector.<Number>):Number
{
var product:Number = 1;
for(var i: uint = 0; i < v.length; i++)
product *= v[i];
return Math.pow(product, 1/v.length);
}
function harmonicMean(v:Vector.<Number>):Number
{
var sum:Number = 0;
for(var i: uint = 0; i < v.length; i++)
sum += 1/v[i];
return v.length/sum;
}
var list:Vector.<Number> = Vector.<Number>([1,2,3,4,5,6,7,8,9,10]);
trace("Arithmetic: ", arithmeticMean(list));
trace("Geometric: ", geometricMean(list));
trace("Harmonic: ", harmonicMean(list));


package Pythagorean_Means is
type Set is array (Positive range <>) of Float;
function Arithmetic_Mean (Data : Set) return Float;
function Geometric_Mean  (Data : Set) return Float;
function Harmonic_Mean   (Data : Set) return Float;
end Pythagorean_Means;


with Ada.Numerics.Generic_Elementary_Functions;
package body Pythagorean_Means is
package Math is new Ada.Numerics.Generic_Elementary_Functions (Float);
function "**" (Left, Right : Float) return Float renames Math."**";

function Arithmetic_Mean (Data : Set) return Float is
Sum : Float := 0.0;
begin
for I in Data'Range loop
Sum := Sum + Data (I);
end loop;
return Sum / Float (Data'Length);
end Arithmetic_Mean;

function Geometric_Mean (Data : Set) return Float is
Product : Float := 1.0;
begin
for I in Data'Range loop
Product := Product * Data (I);
end loop;
return Product**(1.0/Float(Data'Length));
end Geometric_Mean;

function Harmonic_Mean (Data : Set) return Float is
Reciprocal_Sum : Float := 0.0;
begin
for I in Data'Range loop
Reciprocal_Sum := Reciprocal_Sum + Data (I)**(-1);
end loop;
return Float (Data'Length) / Reciprocal_Sum;
end Harmonic_Mean;

end Pythagorean_Means;


with Ada.Text_IO;
with Pythagorean_Means;
procedure Main is
My_Set : Pythagorean_Means.Set := (1.0, 2.0, 3.0, 4.0,  5.0,
6.0, 7.0, 8.0, 9.0, 10.0);
Arithmetic_Mean : Float := Pythagorean_Means.Arithmetic_Mean (My_Set);
Geometric_Mean  : Float := Pythagorean_Means.Geometric_Mean  (My_Set);
Harmonic_Mean   : Float := Pythagorean_Means.Harmonic_Mean   (My_Set);
begin
Ada.Text_IO.Put_Line (Float'Image (Arithmetic_Mean) & " >= " &
Float'Image (Geometric_Mean)  & " >= " &
Float'Image (Harmonic_Mean));
end Main;


## ALGOL 68

{{trans|C}} {{wont work with|ALGOL 68|Standard - argc and argv implementation dependent}} {{works with|ALGOL 68G|Any - tested with release [http://sourceforge.net/projects/algol68/files/algol68g/algol68g-1.18.0/algol68g-1.18.0-9h.tiny.el5.centos.fc11.i386.rpm/download 1.18.0-9h.tiny]}} {{wont work with|ELLA ALGOL 68|Any (with appropriate job cards) - argc and argv implementation dependent}}

main: (
INT count:=0;
LONG REAL f, sum:=0, prod:=1, resum:=0;

FORMAT real = $g(0,4)$; # preferred real format #

FILE fbuf; STRING sbuf; associate(fbuf,sbuf);

BOOL opts := TRUE;

FOR i TO argc DO
IF opts THEN # skip args up to the - token #
opts := argv(i) NE "-"
ELSE
rewind(fbuf); sbuf := argv(i); get(fbuf,f);
count +:= 1;
sum +:= f;
prod *:= f;
resum +:= 1/f
FI
OD;
printf(($"c: "f(real)l"s: "f(real)l"p: "f(real)l"r: "f(real)l$,count,sum,prod,resum));
printf(($"Arithmetic mean = "f(real)l$,sum/count));
printf(($"Geometric mean = "f(real)l$,prod**(1/count)));
printf(($"Harmonic mean = "f(real)l$,count/resum))
)


Lunix command: a68g Averages_Pythagorean_means.a68 - 1 2 3 4 5 6 7 8 9 10 {{out}}


c: 10.0000
s: 55.0000
p: 3628800.0000
r: 2.9290
Arithmetic mean = 5.5000
Geometric mean = 4.5287
Harmonic mean = 3.4142



## ALGOL W

begin
% returns the arithmetic mean of the elements of n from lo to hi %
real procedure arithmeticMean ( real array n ( * ); integer value lo, hi ) ;
begin
real sum;
sum := 0;
for i := lo until hi do sum := sum + n( i );
sum / ( 1 + ( hi - lo ) )
end arithmeticMean ;
% returns the geometric mean of the elements of n from lo to hi %
real procedure geometricMean ( real array n ( * ); integer value lo, hi ) ;
begin
real product;
product := 1;
for i := lo until hi do product := product * n( i );
exp( ln( product ) / ( 1 + ( hi - lo ) ) )
end geometricMean ;
% returns the harminic mean of the elements of n from lo to hi %
real procedure harmonicMean ( real array n ( * ); integer value lo, hi ) ;
begin
real sum;
sum := 0;
for i := lo until hi do sum := sum + ( 1 / n( i ) );
( 1 + ( hi - lo ) ) / sum
end harmonicMean ;

real array v ( 1 :: 10 );
for i := 1 until 10 do v( i ) := i;

r_w := 10; r_d := 5; r_format := "A"; s_w := 0; % set output format %

write( "Arithmetic mean: ", arithmeticMean( v, 1, 10 ) );
write( "Geometric  mean: ",  geometricMean( v, 1, 10 ) );
write( "Harmonic   mean: ",   harmonicMean( v, 1, 10 ) )

end.


{{out}}


Arithmetic mean:    5.50000
Geometric  mean:    4.52872
Harmonic   mean:    3.41417



## APL


arithmetic←{(+/⍵)÷⍴⍵}
geometric←{(×/⍵)*÷⍴⍵}
harmonic←{(⍴⍵)÷(+/÷⍵)}

x←⍳10

arithmetic x
5.5
geometric x
4.528728688
harmonic x
3.414171521


## AppleScript

{{trans|JavaScript}}

-- arithmetic_mean :: [Number] -> Number
on arithmetic_mean(xs)

-- sum :: Number -> Number -> Number
script sum
on |λ|(accumulator, x)
accumulator + x
end |λ|
end script

foldl(sum, 0, xs) / (length of xs)
end arithmetic_mean

-- geometric_mean :: [Number] -> Number
on geometric_mean(xs)

-- product :: Number -> Number -> Number
script product
on |λ|(accumulator, x)
accumulator * x
end |λ|
end script

foldl(product, 1, xs) ^ (1 / (length of xs))
end geometric_mean

-- harmonic_mean :: [Number] -> Number
on harmonic_mean(xs)

-- addInverse :: Number -> Number -> Number
on |λ|(accumulator, x)
accumulator + (1 / x)
end |λ|
end script

(length of xs) / (foldl(addInverse, 0, xs))
end harmonic_mean

-- TEST -----------------------------------------------------------------------
on run
set {A, G, H} to ap({arithmetic_mean, geometric_mean, harmonic_mean}, ¬
{{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}})

{values:{arithmetic:A, geometric:G, harmonic:H}, inequalities:¬
{|A >= G|:A ≥ G}, |G >= H|:G ≥ H}
end run

-- GENERIC FUNCTIONS ----------------------------------------------------------

-- A list of functions applied to a list of arguments
-- (<*> | ap) :: [(a -> b)] -> [a] -> [b]
on ap(fs, xs)
set {nf, nx} to {length of fs, length of xs}
set acc to {}
repeat with i from 1 to nf
tell mReturn(item i of fs)
repeat with j from 1 to nx
set end of acc to |λ|(contents of (item j of xs))
end repeat
end tell
end repeat
return acc
end ap

-- foldl :: (a -> b -> a) -> a -> [b] -> a
on foldl(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from 1 to lng
set v to |λ|(v, item i of xs, i, xs)
end repeat
return v
end tell
end foldl

-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map

-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: Handler -> Script
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn


{{Out}}

{values:{arithmetic:5.5, geometric:4.528728688117, harmonic:3.414171521474},
inequalities:{|A >= G|:true}, |G >= H|:true}


## AutoHotkey

A := ArithmeticMean(1, 10)
G := GeometricMean(1, 10)
H := HarmonicMean(1, 10)

If G Between %H% And %A%
Result := "True"
Else
Result := "False"

MsgBox, %A%n%G%n%H%n%Result%

;---------------------------------------------------------------------------
ArithmeticMean(a, b) { ; of integers a through b
;---------------------------------------------------------------------------
n := b - a + 1
Loop, %n%
Sum += (a + A_Index - 1)
Return, Sum / n
}

;---------------------------------------------------------------------------
GeometricMean(a, b) { ; of integers a through b
;---------------------------------------------------------------------------
n := b - a + 1
Prod := 1
Loop, %n%
Prod *= (a + A_Index - 1)
Return, Prod ** (1 / n)
}

;---------------------------------------------------------------------------
HarmonicMean(a, b) { ; of integers a through b
;---------------------------------------------------------------------------
n := b - a + 1
Loop, %n%
Sum += 1 / (a + A_Index - 1)
Return, n / Sum
}


Message box shows:


5.500000
4.528729
3.414172
True



## AWK

#!/usr/bin/awk -f
{
x  = $1; # value of 1st column A += x; G += log(x); H += 1/x; N++; } END { print "Arithmethic mean: ",A/N; print "Geometric mean : ",exp(G/N); print "Harmonic mean : ",N/H; }  ## BBC BASIC The arithmetic and harmonic means use BBC BASIC's built-in array operations; only the geometric mean needs a loop.  DIM a(9) a() = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 PRINT "Arithmetic mean = " ; FNarithmeticmean(a()) PRINT "Geometric mean = " ; FNgeometricmean(a()) PRINT "Harmonic mean = " ; FNharmonicmean(a()) END DEF FNarithmeticmean(a()) = SUM(a()) / (DIM(a(),1)+1) DEF FNgeometricmean(a()) LOCAL a, I% a = 1 FOR I% = 0 TO DIM(a(),1) a *= a(I%) NEXT = a ^ (1/(DIM(a(),1)+1)) DEF FNharmonicmean(a()) LOCAL b() DIM b(DIM(a(),1)) b() = 1/a() = (DIM(a(),1)+1) / SUM(b())  {{out}} Arithmetic mean = 5.5 Geometric mean = 4.52872869 Harmonic mean = 3.41417152  ## C #include <stdio.h> #include <stdlib.h> // atoi() #include <math.h> // pow() int main(int argc, char* argv[]) { int i, count=0; double f, sum=0.0, prod=1.0, resum=0.0; for (i=1; i<argc; ++i) { f = atof(argv[i]); count++; sum += f; prod *= f; resum += (1.0/f); } //printf(" c:%d\n s:%f\n p:%f\n r:%f\n",count,sum,prod,resum); printf("Arithmetic mean = %f\n",sum/count); printf("Geometric mean = %f\n",pow(prod,(1.0/count))); printf("Harmonic mean = %f\n",count/resum); return 0; }  ## C++ #include <vector> #include <iostream> #include <numeric> #include <cmath> #include <algorithm> double toInverse ( int i ) { return 1.0 / i ; } int main( ) { std::vector<int> numbers ; for ( int i = 1 ; i < 11 ; i++ ) numbers.push_back( i ) ; double arithmetic_mean = std::accumulate( numbers.begin( ) , numbers.end( ) , 0 ) / 10.0 ; double geometric_mean = pow( std::accumulate( numbers.begin( ) , numbers.end( ) , 1 , std::multiplies<int>( ) ), 0.1 ) ; std::vector<double> inverses ; inverses.resize( numbers.size( ) ) ; std::transform( numbers.begin( ) , numbers.end( ) , inverses.begin( ) , toInverse ) ; double harmonic_mean = 10 / std::accumulate( inverses.begin( ) , inverses.end( ) , 0.0 ); //initial value of accumulate must be a double! std::cout << "The arithmetic mean is " << arithmetic_mean << " , the geometric mean " << geometric_mean << " and the harmonic mean " << harmonic_mean << " !\n" ; return 0 ; }  {{out}} The arithmetic mean is 5.5 , the geometric mean 4.52873 and the harmonic mean 3.41417 !  ## C# The standard Linq extension method Average provides arithmetic mean. This example adds two more extension methods for the geometric and harmonic means. {{works with|C sharp|C#|3}} using System; using System.Collections.Generic; using System.Diagnostics; using System.Linq; namespace PythMean { static class Program { static void Main(string[] args) { var nums = from n in Enumerable.Range(1, 10) select (double)n; var a = nums.Average(); var g = nums.Gmean(); var h = nums.Hmean(); Console.WriteLine("Arithmetic mean {0}", a); Console.WriteLine("Geometric mean {0}", g); Console.WriteLine("Harmonic mean {0}", h); Debug.Assert(a >= g && g >= h); } // Geometric mean extension method. static double Gmean(this IEnumerable<double> n) { return Math.Pow(n.Aggregate((s, i) => s * i), 1.0 / n.Count()); } // Harmonic mean extension method. static double Hmean(this IEnumerable<double> n) { return n.Count() / n.Sum(i => 1.0 / i); } } }  {{out}}  Arithmetic mean 5.5 Geometric mean 4.52872868811677 Harmonic mean 3.41417152147406  ## CoffeeScript a = [ 1..10 ] arithmetic_mean = (a) -> a.reduce(((s, x) -> s + x), 0) / a.length geometic_mean = (a) -> Math.pow(a.reduce(((s, x) -> s * x), 1), (1 / a.length)) harmonic_mean = (a) -> a.length / a.reduce(((s, x) -> s + 1 / x), 0) A = arithmetic_mean a G = geometic_mean a H = harmonic_mean a console.log "A = ", A, " G = ", G, " H = ", H console.log "A >= G : ", A >= G, " G >= H : ", G >= H  {{out}} A = 5.5 G = 4.528728688116765 H = 3.414171521474055 A >= G : true G >= H : true  ## Common Lisp (defun generic-mean (nums reduce-op final-op) (funcall final-op (reduce reduce-op nums))) (defun a-mean (nums) (generic-mean nums #'+ (lambda (x) (/ x (length nums))))) (defun g-mean (nums) (generic-mean nums #'* (lambda (x) (expt x (/ 1 (length nums)))))) (defun h-mean (nums) (generic-mean nums (lambda (x y) (+ x (/ 1 y))) (lambda (x) (/ (length nums) x)))) (let ((numbers (loop for i from 1 to 10 collect i))) (let ((a-mean (a-mean numbers)) (g-mean (g-mean numbers)) (h-mean (h-mean numbers))) (assert (> a-mean g-mean h-mean)) (format t "a-mean ~a~%" a-mean) (format t "g-mean ~a~%" g-mean) (format t "h-mean ~a~%" h-mean)))  ## Clojure (use '[clojure.contrib.math :only (expt)]) (defn a-mean [coll] (/ (apply + coll) (count coll))) (defn g-mean [coll] (expt (apply * coll) (/ (count coll)))) (defn h-mean [coll] (/ (count coll) (apply + (map / coll)))) (let [numbers (range 1 11) a (a-mean numbers) g (g-mean numbers) h (h-mean numbers)] (println a ">=" g ">=" h) (>= a g h))  ## D The output for the harmonic mean is wrong. import std.stdio, std.algorithm, std.range, std.functional; auto aMean(T)(T data) pure nothrow @nogc { return data.sum / data.length; } auto gMean(T)(T data) pure /*@nogc*/ { return data.reduce!q{a * b} ^^ (1.0 / data.length); } auto hMean(T)(T data) pure /*@nogc*/ { return data.length / data.reduce!q{ 1.0 / a + b }; } void main() { immutable m = [adjoin!(hMean, gMean, aMean)(iota(1.0L, 11.0L))[]]; writefln("%(%.19f %)", m); assert(m.isSorted); }  {{out}} 0.9891573712076470036 4.5287286881167647619 5.5000000000000000000  ## Delphi program AveragesPythagoreanMeans; {$APPTYPE CONSOLE}

uses Types, Math;

function ArithmeticMean(aArray: TDoubleDynArray): Double;
var
lValue: Double;
begin
Result := 0;
for lValue in aArray do
Result := Result + lValue;
if Result > 0 then
Result := Result / Length(aArray);
end;

function GeometricMean(aArray: TDoubleDynArray): Double;
var
lValue: Double;
begin
Result := 1;
for lValue in aArray do
Result := Result * lValue;
Result := Power(Result, 1 / Length(aArray));
end;

function HarmonicMean(aArray: TDoubleDynArray): Double;
var
lValue: Double;
begin
Result := 0;
for lValue in aArray do
Result := Result + 1 / lValue;
Result := Length(aArray) / Result;
end;

var
lSourceArray: TDoubleDynArray;
AMean, GMean, HMean: Double;
begin
lSourceArray := TDoubleDynArray.Create(1,2,3,4,5,6,7,8,9,10);
AMean := ArithmeticMean(lSourceArray));
GMean := GeometricMean(lSourceArray));
HMean := HarmonicMean(lSourceArray));
if (AMean >= GMean) and (GMean >= HMean) then
Writeln(AMean, " ≥ ", GMean, " ≥ ", HMean)
else
writeln("Error!");
end.


## E

Given that we're defining all three together, it makes sense to express their regularities:

def makeMean(base, include, finish) {
return def mean(numbers) {
var count := 0
var acc := base
for x in numbers {
acc := include(acc, x)
count += 1
}
return finish(acc, count)
}
}

def A := makeMean(0, fn b,x { b+x   }, fn acc,n { acc / n      })
def G := makeMean(1, fn b,x { b*x   }, fn acc,n { acc ** (1/n) })
def H := makeMean(0, fn b,x { b+1/x }, fn acc,n { n / acc      })

? A(1..10)
# value: 5.5

? G(1..10)
# value: 4.528728688116765

? H(1..10)
# value: 3.414171521474055


## EchoLisp


(define (A xs) (// (for/sum ((x xs)) x) (length xs)))

(define (G xs) (expt (for/product ((x xs)) x) (// (length xs))))

(define (H xs) (// (length xs) (for/sum ((x xs)) (// x))))

(define xs (range 1 11))
(and (>= (A xs) (G xs)) (>= (G xs) (H xs)))
→ #t



## Elixir

defmodule Means do
def arithmetic(list) do
Enum.sum(list) / length(list)
end
def geometric(list) do
:math.pow(Enum.reduce(list, &(*/2)), 1 / length(list))
end
def harmonic(list) do
1 / arithmetic(Enum.map(list, &(1 / &1)))
end
end

list = Enum.to_list(1..10)
IO.puts "Arithmetic mean: #{am = Means.arithmetic(list)}"
IO.puts "Geometric mean:  #{gm = Means.geometric(list)}"
IO.puts "Harmonic mean:   #{hm = Means.harmonic(list)}"
IO.puts "(#{am} >= #{gm} >= #{hm}) is #{am >= gm and gm >= hm}"


{{out}}


Arithmetic mean: 5.5
Geometric mean:  4.528728688116765
Harmonic mean:   3.414171521474055
(5.5 >= 4.528728688116765 >= 3.414171521474055) is true



## Erlang

%% Author: Abhay Jain <abhay_1303@yahoo.co.in>

-module(mean_calculator).
-export([find_mean/0]).

find_mean() ->
%% This is function calling. First argument is the the beginning number
%% and second argument is the initial value of sum for AM & HM and initial value of product for GM.
arithmetic_mean(1, 0),
geometric_mean(1, 1),
harmonic_mean(1, 0).

%% Function to calculate Arithmetic Mean
arithmetic_mean(Number, Sum) when Number > 10 ->
AM = Sum / 10,
io:format("Arithmetic Mean ~p~n", [AM]);
arithmetic_mean(Number, Sum) ->
NewSum = Sum + Number,
arithmetic_mean(Number+1, NewSum).

%% Function to calculate Geometric Mean
geometric_mean(Number, Product) when Number > 10 ->
GM = math:pow(Product, 0.1),
io:format("Geometric Mean ~p~n", [GM]);
geometric_mean(Number, Product) ->
NewProd = Product * Number,
geometric_mean(Number+1, NewProd).

%% Function to calculate Harmonic Mean
harmonic_mean(Number, Sum) when Number > 10 ->
HM = 10 / Sum,
io:format("Harmonic Mean ~p~n", [HM]);
harmonic_mean(Number, Sum) ->
NewSum = Sum + (1/Number),
harmonic_mean(Number+1, NewSum).


{{out}}

Arithmetic Mean 5.5
Geometric Mean 4.528728688116765
Harmonic Mean 3.414171521474055


## ERRE

PROGRAM MEANS

DIM A[9]

PROCEDURE ARITHMETIC_MEAN(A[]->M) LOCAL S,I% NEL%=UBOUND(A,1) S=0 FOR I%=0 TO NEL% DO S+=A[I%] END FOR M=S/(NEL%+1) END PROCEDURE

PROCEDURE GEOMETRIC_MEAN(A[]->M) LOCAL S,I% NEL%=UBOUND(A,1) S=1 FOR I%=0 TO NEL% DO S*=A[I%] END FOR M=S^(1/(NEL%+1)) END PROCEDURE

PROCEDURE HARMONIC_MEAN(A[]->M) LOCAL S,I% NEL%=UBOUND(A,1) S=0 FOR I%=0 TO NEL% DO S+=1/A[I%] END FOR M=(NEL%+1)/S END PROCEDURE

BEGIN A[]=(1,2,3,4,5,6,7,8,9,10) ARITHMETIC_MEAN(A[]->M) PRINT("Arithmetic mean = ";M) GEOMETRIC_MEAN(A[]->M) PRINT("Geometric mean = ";M) HARMONIC_MEAN(A[]->M) PRINT("Harmonic mean = ";M) END PROGRAM



## Euler Math Toolbox

Euler Math Toolbox

>function A(x) := mean(x)
>function G(x) := exp(mean(log(x)))
>function H(x) := 1/mean(1/x)
>x=1:10; A(x), G(x), H(x)
5.5
4.52872868812
3.41417152147



Alternatively, e.g.,


>function G(x) := prod(x)^(1/length(x))



## Euphoria

function arithmetic_mean(sequence s)
atom sum
if length(s) = 0 then
return 0
else
sum = 0
for i = 1 to length(s) do
sum += s[i]
end for
return sum/length(s)
end if
end function

function geometric_mean(sequence s)
atom p
p = 1
for i = 1 to length(s) do
p *= s[i]
end for
return power(p,1/length(s))
end function

function harmonic_mean(sequence s)
atom sum
if length(s) = 0 then
return 0
else
sum = 0
for i = 1 to length(s) do
sum += 1/s[i]
end for
return length(s) / sum
end if
end function

function true_or_false(atom x)
if x then
return "true"
else
return "false"
end if
end function

constant s = {1,2,3,4,5,6,7,8,9,10}
constant arithmetic = arithmetic_mean(s),
geometric = geometric_mean(s),
harmonic = harmonic_mean(s)
printf(1,"Arithmetic: %g\n", arithmetic)
printf(1,"Geometric: %g\n", geometric)
printf(1,"Harmonic: %g\n", harmonic)
printf(1,"Arithmetic>=Geometric>=Harmonic: %s\n",
{true_or_false(arithmetic>=geometric and geometric>=harmonic)})


{{out}}

Arithmetic: 5.5
Geometric: 4.52873
Harmonic: 3.41417
Arithmetic>=Geometric>=Harmonic: true



## Excel

Use the functions : AVERAGE, GEOMEAN and HARMEAN


=AVERAGE(1;2;3;4;5;6;7;8;9;10)
=GEOMEAN(1;2;3;4;5;6;7;8;9;10)
=HARMEAN(1;2;3;4;5;6;7;8;9;10)



{{out}}


5.5
4.528728688
3,414171521



let P = [1.0; 2.0; 3.0; 4.0; 5.0; 6.0; 7.0; 8.0; 9.0; 10.0]

let arithmeticMean (x : float list) =
x |> List.sum
|> (fun acc -> acc / float (List.length(x)))

let geometricMean (x: float list) =
x |> List.reduce (*)
|> (fun acc -> Math.Pow(acc, 1.0 / (float (List.length(x)))))

let harmonicMean (x: float list) =
x |> List.map (fun a -> 1.0 / a)
|> List.sum
|> (fun acc -> float (List.length(x)) / acc)

printfn "Arithmetic Mean: %A" (arithmeticMean P)
printfn "Geometric Mean: %A" (geometricMean P)
printfn "Harmonic Mean: %A" (harmonicMean P)


## Factor

: a-mean ( seq -- mean )
[ sum ] [ length ] bi / ;

: g-mean ( seq -- mean )
[ product ] [ length recip ] bi ^ ;

: h-mean ( seq -- mean )
[ length ] [ [ recip ] map-sum ] bi / ;


( scratchpad ) 10 [1,b] [ a-mean ] [ g-mean ] [ h-mean ] tri "%f >= %f >= %f\n" printf 5.500000 >= 4.528729 >= 3.414172

## Fantom


class Main
{
static Float arithmeticMean (Int[] nums)
{
if (nums.size == 0) return 0.0f
sum := 0
nums.each |n| { sum += n }
return sum.toFloat / nums.size
}

static Float geometricMean (Int[] nums)
{
if (nums.size == 0) return 0.0f
product := 1
nums.each |n| { product *= n }
return product.toFloat.pow(1f/nums.size)
}

static Float harmonicMean (Int[] nums)
{
if (nums.size == 0) return 0.0f
reciprocals := 0f
nums.each |n| { reciprocals += 1f / n }
return nums.size.toFloat / reciprocals
}

public static Void main ()
{
items := (1..10).toList
// display results
echo (arithmeticMean (items))
echo (geometricMean (items))
echo (harmonicMean (items))
// check given relation
if ((arithmeticMean (items) >= geometricMean (items)) &&
(geometricMean (items) >= harmonicMean (items)))
echo ("relation holds")
else
echo ("relation failed")
}
}



## Forth

: famean ( faddr n -- f )
0e
tuck floats bounds do
i f@ f+
float +loop
0 d>f f/ ;

: fgmean ( faddr n -- f )
1e
tuck floats bounds do
i f@ f*
float +loop
0 d>f 1/f f** ;

: fhmean ( faddr n -- f )
dup 0 d>f  0e
floats bounds do
i f@ 1/f f+
float +loop
f/ ;

create test 1e f, 2e f, 3e f, 4e f, 5e f, 6e f, 7e f, 8e f, 9e f, 10e f,
test 10 famean fdup f.
test 10 fgmean fdup fdup f.
test 10 fhmean fdup f.
( A G G H )
f>= . f>= .  \ -1 -1


## Fortran

{{works with|Fortran|90}}

program Mean

real :: a(10) = (/ (i, i=1,10) /)
real :: amean, gmean, hmean

amean = sum(a) / size(a)
gmean = product(a)**(1.0/size(a))
hmean = size(a) / sum(1.0/a)

if ((amean < gmean) .or. (gmean < hmean)) then
print*, "Error!"
else
print*, amean, gmean, hmean
end if

end program Mean


## FreeBASIC


' 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



{{out}}


Arithmetic mean is : 5.5
Geometric mean is  : 4.528728688116765
Harmonic mean is   : 3.414171521474055



## FunL

import lists.zip

def
mean( s, 0 ) = product( s )^(1/s.length())
mean( s, p ) = (1/s.length() sum( x^p | x <- s ))^(1/p)

def
monotone( [_], _ ) = true
monotone( a1:a2:as, p ) = p( a1, a2 ) and monotone( a2:as, p )

means = [mean( 1..10, m ) | m <- [1, 0, -1]]

for (m, l) <- zip( means, ['Arithmetic', 'Geometric', 'Harmonic'] )
println( "$l:$m" + (if m is Rational then " or ${m.doubleValue()}" else '') ) println( monotone(means, (>=)) )  {{out}}  Arithmetic: 11/2 or 5.5 Geometric: 4.528728688116765 Harmonic: 25200/7381 or 3.414171521474055 true  ## Futhark  fun arithmetic_mean(as: [n]f64): f64 = reduce (+) 0.0 (map (/f64(n)) as) fun geometric_mean(as: [n]f64): f64 = reduce (*) 1.0 (map (**(1.0/f64(n))) as) fun harmonic_mean(as: [n]f64): f64 = f64(n) / reduce (+) 0.0 (map (1.0/) as) fun main(as: [n]f64): (f64,f64,f64) = (arithmetic_mean as, geometric_mean as, harmonic_mean as)  ## GAP # The first two work with rationals or with floats # (but bear in mind that support of floating point is very poor in GAP) mean := v -> Sum(v) / Length(v); harmean := v -> Length(v) / Sum(v, Inverse); geomean := v -> EXP_FLOAT(Sum(v, LOG_FLOAT) / Length(v)); mean([1 .. 10]); # 11/2 harmean([1 .. 10]); # 25200/7381 v := List([1..10], FLOAT_INT);; mean(v); # 5.5 harmean(v); # 3.41417 geomean(v); # 4.52873  ## Go package main import ( "fmt" "math" ) func main() { sum, sumr, prod := 0., 0., 1. for n := 1.; n <= 10; n++ { sum += n sumr += 1 / n prod *= n } a, g, h := sum/10, math.Pow(prod, .1), 10/sumr fmt.Println("A:", a, "G:", g, "H:", h) fmt.Println("A >= G >= H:", a >= g && g >= h) }  {{out}}  A: 5.5 G: 4.528728688116765 H: 3.414171521474055 A >= G >= H: true  ## Groovy Solution: def arithMean = { list -> list == null \ ? null \ : list.empty \ ? 0 \ : list.sum() / list.size() } def geomMean = { list -> list == null \ ? null \ : list.empty \ ? 1 \ : list.inject(1) { prod, item -> prod*item } ** (1 / list.size()) } def harmMean = { list -> list == null \ ? null \ : list.empty \ ? 0 \ : list.size() / list.collect { 1.0/it }.sum() }  Test: def list = 1..10 def A = arithMean(list) def G = geomMean(list) assert A >= G def H = harmMean(list) assert G >= H println """ list:${list}
A: ${A} G:${G}
(show . and) $zipWith (>=) xs (tail xs) ]  {{Out}} ("Arithmetic",5.5)("Geometric",4.528728688116765)("Harmonic",3.414171521474055) a >= g >= h is True  ## HicEst AGH = ALIAS( A, G, H ) ! named vector elements AGH = (0, 1, 0) DO i = 1, 10 A = A + i G = G * i H = H + 1/i ENDDO AGH = (A/10, G^0.1, 10/H) WRITE(ClipBoard, Name) AGH, "Result = " // (A>=G) * (G>=H)  ! A=5.5; G=4.528728688; H=3.414171521; Result = 1; =={{header|Icon}} and {{header|Unicon}}== link numbers # for a/g/h means procedure main() every put(x := [], 1 to 10) writes("x := [ "); every writes(!x," "); write("]") write("Arithmetic mean:", a := amean!x) write("Geometric mean:",g := gmean!x) write("Harmonic mean:", h := hmean!x) write(" a >= g >= h is ", if a >= g >= h then "true" else "false") end  {{libheader|Icon Programming Library}} [http://www.cs.arizona.edu/icon/library/src/procs/numbers.icn numbers:amean, numbers:gmean, and numbers:hmean] are shown below: procedure amean(L[]) #: arithmetic mean local m if *L = 0 then fail m := 0.0 every m +:= !L return m / *L end procedure gmean(L[]) #: geometric mean local m if *L = 0 then fail m := 1.0 every m *:= !L m := abs(m) if m > 0.0 then return exp (log(m) / *L) else fail end procedure hmean(L[]) #: harmonic mean local m, r if *L = 0 then fail m := 0.0 every r := !L do { if r = 0.0 then fail else m +:= 1.0 / r } return *L / m end  {{out}} #means.exe x := [ 1 2 3 4 5 6 7 8 9 10 ] Arithmetic mean:5.5 Geometric mean:4.528728688116765 Harmonic mean:3.414171521474055 a >= g >= h is true  =={{header|IS-BASIC}}== 100 PROGRAM "Averages.bas" 110 NUMERIC ARR(1 TO 10) 120 FOR I=LBOUND(ARR) TO UBOUND(ARR) 130 LET ARR(I)=I 140 NEXT 150 PRINT "Arithmetic mean =";ARITHM(ARR) 160 PRINT "Geometric mean =";GEOMETRIC(ARR) 170 PRINT "Harmonic mean =";HARMONIC(ARR) 180 DEF ARITHM(REF A) 190 LET T=0 200 FOR I=LBOUND(A) TO UBOUND(A) 210 LET T=T+A(I) 220 NEXT 230 LET ARITHM=T/SIZE(A) 240 END DEF 250 DEF GEOMETRIC(REF A) 260 LET T=1 270 FOR I=LBOUND(A) TO UBOUND(A) 280 LET T=T*A(I) 290 NEXT 300 LET GEOMETRIC=T^(1/SIZE(A)) 310 END DEF 320 DEF HARMONIC(REF A) 330 LET T=0 340 FOR I=LBOUND(A) TO UBOUND(A) 350 LET T=T+(1/A(I)) 360 NEXT 370 LET HARMONIC=SIZE(A)/T 380 END DEF  ## J '''Solution:''' j amean=: +/ % # gmean=: # %: */ hmean=: amean&.:%  '''Example Usage:'''  (amean , gmean , hmean) >: i. 10 5.5 4.528729 3.414172 assert 2 >:/\ (amean , gmean , hmean) >: i. 10 NB. check amean >= gmean and gmean >= hmean  Note that gmean could have instead been defined as mean under logarithm, for example: gmean=:amean&.:^.  (and this variant should probably be preferred - especially if the argument list is long, to avoid problems with floating point infinity.) ## Java import java.util.Arrays; import java.util.List; public class PythagoreanMeans { public static double arithmeticMean(List<Double> numbers) { if (numbers.isEmpty()) return Double.NaN; double mean = 0.0; for (Double number : numbers) { mean += number; } return mean / numbers.size(); } public static double geometricMean(List<Double> numbers) { if (numbers.isEmpty()) return Double.NaN; double mean = 1.0; for (Double number : numbers) { mean *= number; } return Math.pow(mean, 1.0 / numbers.size()); } public static double harmonicMean(List<Double> numbers) { if (numbers.isEmpty() || numbers.contains(0.0)) return Double.NaN; double mean = 0.0; for (Double number : numbers) { mean += (1.0 / number); } return numbers.size() / mean; } public static void main(String[] args) { Double[] array = {1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0}; List<Double> list = Arrays.asList(array); double arithmetic = arithmeticMean(list); double geometric = geometricMean(list); double harmonic = harmonicMean(list); System.out.format("A = %f G = %f H = %f%n", arithmetic, geometric, harmonic); System.out.format("A >= G is %b, G >= H is %b%n", (arithmetic >= geometric), (geometric >= harmonic)); } }  {{out}} A = 5.500000 G = 4.528729 H = 3.414172 A >= G is true, G >= H is true  {{works with|Java|1.8}} We can rewrite the 3 methods using the new JAVA Stream API:  public static double arithmAverage(double array[]){ if (array == null ||array.length == 0) { return 0.0; } else { return DoubleStream.of(array).average().getAsDouble(); } } public static double geomAverage(double array[]){ if (array == null ||array.length == 0) { return 0.0; } else { double aver = DoubleStream.of(array).reduce(1, (x, y) -> x * y); return Math.pow(aver, 1.0 / array.length); } } public static double harmAverage(double array[]){ if (array == null ||array.length == 0) { return 0.0; } else { double aver = DoubleStream.of(array) // remove null values .filter(n -> n > 0.0) // generate 1/n array .map( n-> 1.0/n) // accumulating .reduce(0, (x, y) -> x + y); // just this reduce is not working- need to do in 2 steps // .reduce(0, (x, y) -> 1.0/x + 1.0/y); return array.length / aver ; } }  ## JavaScript ### ES5 (function () { 'use strict'; // arithmetic_mean :: [Number] -> Number function arithmetic_mean(ns) { return ( ns.reduce( // sum function (sum, n) { return (sum + n); }, 0 ) / ns.length ); } // geometric_mean :: [Number] -> Number function geometric_mean(ns) { return Math.pow( ns.reduce( // product function (product, n) { return (product * n); }, 1 ), 1 / ns.length ); } // harmonic_mean :: [Number] -> Number function harmonic_mean(ns) { return ( ns.length / ns.reduce( // sum of inverses function (invSum, n) { return (invSum + (1 / n)); }, 0 ) ); } var values = [arithmetic_mean, geometric_mean, harmonic_mean] .map(function (f) { return f([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]); }), mean = { Arithmetic: values[0], // arithmetic Geometric: values[1], // geometric Harmonic: values[2] // harmonic } return JSON.stringify({ values: mean, test: "is A >= G >= H ? " + ( mean.Arithmetic >= mean.Geometric && mean.Geometric >= mean.Harmonic ? "yes" : "no" ) }, null, 2); })();  {{Out}} { "values": { "Arithmetic": 5.5, "Geometric": 4.528728688116765, "Harmonic": 3.414171521474055 }, "test": "is A >= G >= H ? yes" }  ### ES6 (() => { // arithmeticMean :: [Number] -> Number const arithmeticMean = xs => foldl((sum, n) => sum + n, 0, xs) / length(xs); // geometricMean :: [Number] -> Number const geometricMean = xs => raise(foldl((product, x) => product * x, 1, xs), 1 / length(xs)); // harmonicMean :: [Number] -> Number const harmonicMean = xs => length(xs) / foldl((invSum, n) => invSum + (1 / n), 0, xs); // GENERIC FUNCTIONS ------------------------------------------------------ // A list of functions applied to a list of arguments // <*> :: [(a -> b)] -> [a] -> [b] const ap = (fs, xs) => // [].concat.apply([], fs.map(f => // [].concat.apply([], xs.map(x => [f(x)])))); // foldl :: (b -> a -> b) -> b -> [a] -> b const foldl = (f, a, xs) => xs.reduce(f, a); // length :: [a] -> Int const length = xs => xs.length; // mapFromList :: [(k, v)] -> Dictionary const mapFromList = kvs => foldl((a, [k, v]) => (a[(typeof k === 'string' && k) || show(k)] = v, a), {}, kvs); // raise :: Num -> Int -> Num const raise = (n, e) => Math.pow(n, e); // show :: a -> String // show :: a -> Int -> String const show = (...x) => JSON.stringify.apply( null, x.length > 1 ? [x[0], null, x[1]] : x ); // zip :: [a] -> [b] -> [(a,b)] const zip = (xs, ys) => xs.slice(0, Math.min(xs.length, ys.length)) .map((x, i) => [x, ys[i]]); // TEST ------------------------------------------------------------------- // mean :: Dictionary const mean = mapFromList(zip( ['Arithmetic', 'Geometric', 'Harmonic'], ap([arithmeticMean, geometricMean, harmonicMean], [ [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] ]) )); return show({ values: mean, test: is A >= G >= H ?${mean.Arithmetic >= mean.Geometric &&
mean.Geometric >= mean.Harmonic ? "yes" : "no"}
}, 2);
})();


{{Out}}

{
"values": {
"Arithmetic": 5.5,
"Geometric": 4.528728688116765,
"Harmonic": 3.414171521474055
},
"test": "is A >= G >= H ? yes"
}


## jq

def amean: add/length;

def gmean:  (logProduct / length) | exp;

def hmean: length / (map(1/.) | add);

[range(1;11) ] | [amean, gmean, hmean] as $ans | ($ans[],
"amean > gmean > hmean => \($ans[0] >$ans[1] and $ans[1] >$ans[2] )" )



{{Out}}

5.5
4.528728688116766
3.414171521474055
"amean > gmean > hmean => true"


## Julia

Julia has a mean function to compute the arithmetic mean of a collections of numbers. We can redefine it as follows.

amean(A) = sum(A)/length(A)

gmean(A) = prod(A)^(1/length(A))

hmean(A) = length(A)/sum(1./A)


{{Out}}

julia> map(f-> f(1:10), [amean, gmean, hmean])
3-element Array{Float64,1}:
5.5
4.52873
3.41417
julia> ans[1] > ans[2] > ans[3]
true


## K


am:{(+/x)%#x}
gm:{(*/x)^(%#x)}
hm:{(#x)%+/%:'x}

{(am x;gm x;hm x)} 1+!10
5.5 4.528729 3.414172



## Kotlin

.geometricMean() =
if (isEmpty()) Double.NaN
else Math.pow(reduce { n1, n2 -> n1 * n2 }, 1.0 / size)

fun Collection<Double>.harmonicMean() =
if (isEmpty() || contains(0.0)) Double.NaN
else size / reduce { n1, n2 -> n1 + 1.0 / n2 }

fun main(args: Array<String>) {
val list = listOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0)
val a = list.average()  // arithmetic mean
val g = list.geometricMean()
val h = list.harmonicMean()
println("A = %f  G = %f  H = %f".format(a, g, h))
println("A >= G is %b, G >= H is %b".format(a >= g, g >= h))
require(g in h..a)
}


{{out}}

A = 5.500000  G = 4.528729  H = 3.414172
A >= G is true, G >= H is true


## Lasso

define arithmetic_mean(a::staticarray)::decimal => {
//sum of the list divided by its length
return (with e in #a sum #e) / decimal(#a->size)
}
define geometric_mean(a::staticarray)::decimal => {
// The geometric mean is the nth root of the product of the list
local(prod = 1)
with e in #a do => { #prod *= #e }
return math_pow(#prod,1/decimal(#a->size))
}
define harmonic_mean(a::staticarray)::decimal => {
// The harmonic mean is n divided by the sum of the reciprocal of each item in the list
return decimal(#a->size)/(with e in #a sum 1/decimal(#e))
}

arithmetic_mean(generateSeries(1,10)->asStaticArray)
geometric_mean(generateSeries(1,10)->asStaticArray)
harmonic_mean(generateSeries(1,10)->asStaticArray)


{{out}}

5.500000
4.528729
3.414172


## Liberty BASIC

for i = 1 to 10
a = a + i
next
ArithmeticMean = a/10

b = 1
for i = 1 to 10
b = b * i
next
GeometricMean = b ^ (1/10)

for i = 1 to 10
c = c + (1/i)
next
HarmonicMean = 10/c

print "ArithmeticMean: ";ArithmeticMean
print "Geometric Mean: ";GeometricMean
print "Harmonic Mean: ";HarmonicMean

if (ArithmeticMean>=GeometricMean) and (GeometricMean>=HarmonicMean) then
print "True"
else
print "False"
end if


to compute_means :count
local "sum
make "sum     0
local "product
make "product 1
local "reciprocal_sum
make "reciprocal_sum  0

repeat :count [
make "sum sum :sum repcount
make "product product :product repcount
make "reciprocal_sum sum :reciprocal_sum (quotient repcount)
]

output (sentence (quotient :sum :count) (power :product (quotient :count))
(quotient :count :reciprocal_sum))
end

make "means compute_means 10
print sentence [Arithmetic mean is] item 1 :means
print sentence [Geometric mean is] item 2 :means
print sentence [Harmonic mean is] item 3 :means
bye


## Lua

function fsum(f, a, ...) return a and f(a) + fsum(f, ...) or 0 end
function pymean(t, f, finv) return finv(fsum(f, unpack(t)) / #t) end
nums = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

--arithmetic
a = pymean(nums, function(n) return n end, function(n) return n end)
--geometric
g = pymean(nums, math.log, math.exp)
--harmonic
h = pymean(nums, function(n) return 1/n end, function(n) return 1/n end)
print(a, g, h)
assert(a >= g and g >= h)


## M2000 Interpreter

Dimension(m,0) is the base (lower bound) for each dimension in an array, and can be 0 or 1. Len(a) or len(M()) return length of a pointer to array and an array, as number of array elements. For one dimension arrays len() is equal to Dimension(m(),1) where 1 is the first dimension Dim A(10,10) : Print Len(A())=100


Module CheckIt {
sum=lambda -> {
if len(m)=0 then =0 : exit
sum=Array(m, Dimension(m,0))
If len(m)=1 then =sum : exit
k=each(m,2,-1)
While k {
sum+=Array(k)
}
=sum
}
mean=lambda sum (a as array) ->{
=sum(a)/len(a)
}
prod=lambda -> {
m=array
if len(m)=0 then =0 : exit
prod=Array(m, Dimension(m,0))
If len(m)=1 then =prod : exit
k=each(m,2,-1)
While k {
prod*=Array(k)
}
=prod
}
geomean=lambda prod (a as array) -> {
=prod(a)^(1/len(a))
}
harmomean=lambda (a as array) -> {
if len(a)=0 then =0 : exit
sum=1/Array(a, Dimension(a,0))
If len(a)=1 then =1/sum : exit
k=each(a,2,-1)
While k {
sum+=1/Array(k)
}
=len(a)/sum
}
Print sum((1,2,3,4,5))=15
Print prod((1,2,3,4,5))=120
Print mean((1,2,3,4,5))==3
\\ use == to apply rounding before comparison
Print geomean((1,2,3,4,5))==2.60517108469735
Print harmomean((1,2,3,4,5))==2.18978102189784
Generator =lambda x=1 ->{=x : x++}
dim a(10)<<Generator()
Print mean(a())==5.5
Print geomean(a())==4.52872868811677
Print harmomean(a())==3.41417152147412
}
CheckIt



## Maple

x := [ seq( 1 .. 10 ) ];
Means := proc( x )
uses Statistics;
return Mean( x ), GeometricMean( x ), HarmonicMean( x );
end proc:
Arithmeticmean, Geometricmean, Harmonicmean := Means( x );

is( Arithmeticmean >= Geometricmean and Geometricmean >= Harmonicmean );



{{out}}


Arithmeticmean, Geometricmean, Harmonicmean := 5.50000000000000, 4.52872868811677, 3.41417152147406

true



Print["{Arithmetic Mean, Geometric Mean, Harmonic Mean} = ",
N@Through[{Mean, GeometricMean, HarmonicMean}[Range@10]]]


{{out}}

{Arithmetic Mean, Geometric Mean, Harmonic Mean} = {5.5,4.52873,3.41417}


## MATLAB

function [A,G,H] = pythagoreanMeans(list)

A = mean(list);
G = geomean(list);
H = harmmean(list);

end


A solution that works for both, Matlab and Octave, is this

function [A,G,H] = pythagoreanMeans(list)
A = mean(list);           % arithmetic mean
G = exp(mean(log(list))); % geometric mean
H = 1./mean(1./list);     % harmonic mean
end


Solution:

 [A,G,H]=pythagoreanMeans((1:10))

A =

5.500000000000000

G =

4.528728688116765

H =

3.414171521474055


## Maxima

/* built-in */
L: makelist(i, i, 1, 10)$mean(L), numer; /* 5.5 */ geometric_mean(L), numer; /* 4.528728688116765 */ harmonic_mean(L), numer; /* 3.414171521474055 */  =={{header|Modula-2}}== MODULE PythagoreanMeans; FROM FormatString IMPORT FormatString; FROM LongMath IMPORT power; FROM LongStr IMPORT RealToStr; FROM Terminal IMPORT WriteString,WriteLn,ReadChar; PROCEDURE ArithmeticMean(numbers : ARRAY OF LONGREAL) : LONGREAL; VAR i,cnt : CARDINAL; mean : LONGREAL; BEGIN mean := 0.0; cnt := 0; FOR i:=0 TO HIGH(numbers) DO mean := mean + numbers[i]; INC(cnt); END; RETURN mean / LFLOAT(cnt) END ArithmeticMean; PROCEDURE GeometricMean(numbers : ARRAY OF LONGREAL) : LONGREAL; VAR i,cnt : CARDINAL; mean : LONGREAL; BEGIN mean := 1.0; cnt := 0; FOR i:=0 TO HIGH(numbers) DO mean := mean * numbers[i]; INC(cnt); END; RETURN power(mean, 1.0 / LFLOAT(cnt)) END GeometricMean; PROCEDURE HarmonicMean(numbers : ARRAY OF LONGREAL) : LONGREAL; VAR i,cnt : CARDINAL; mean : LONGREAL; BEGIN mean := 0.0; cnt := 0; FOR i:=0 TO HIGH(numbers) DO mean := mean + ( 1.0 / numbers[i]); INC(cnt); END; RETURN LFLOAT(cnt) / mean END HarmonicMean; CONST Size = 10; TYPE DA = ARRAY[1..Size] OF LONGREAL; VAR buf : ARRAY[0..63] OF CHAR; array : DA; arithmetic,geometric,harmonic : LONGREAL; BEGIN array := DA{1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0}; arithmetic := ArithmeticMean(array); geometric := GeometricMean(array); harmonic := HarmonicMean(array); WriteString("A = "); RealToStr(arithmetic, buf); WriteString(buf); WriteString(" G = "); RealToStr(geometric, buf); WriteString(buf); WriteString(" H = "); RealToStr(harmonic, buf); WriteString(buf); WriteLn; FormatString("A >= G is %b, G >= H is %b\n", buf, arithmetic >= geometric, geometric >= harmonic); WriteString(buf); ReadChar END PythagoreanMeans.  ## MUMPS Pyth(n) New a,ii,g,h,x For ii=1:1:n set x(ii)=ii ; ; Average Set a=0 For ii=1:1:n Set a=a+x(ii) Set a=a/n ; ; Geometric Set g=1 For ii=1:1:n Set g=g*x(ii) Set g=g**(1/n) ; ; Harmonic Set h=0 For ii=1:1:n Set h=1/x(ii)+h Set h=n/h ; Write !,"Pythagorean means for 1..",n,":",! Write "Average = ",a," >= Geometric ",g," >= harmonic ",h,! Quit Do Pyth(10) Pythagorean means for 1..10: Average = 5.5 >= Geometric 4.528728688116178495 >= harmonic 3.414171521474055006  ## NetRexx {{trans|ooRexx}} /* NetRexx */ options replace format comments java crossref symbols nobinary numeric digits 20 a1 = ArrayList(Arrays.asList([Rexx 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0])) say "Arithmetic =" arithmeticMean(a1)", Geometric =" geometricMean(a1)", Harmonic =" harmonicMean(a1) return -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ method arithmeticMean(numbers = java.util.List) public static returns Rexx -- somewhat arbitrary return for ooRexx if numbers.isEmpty then return "NaN" mean = 0 number = Rexx loop number over numbers mean = mean + number end return mean / numbers.size -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ method geometricMean(numbers = java.util.List) public static returns Rexx -- somewhat arbitrary return for ooRexx if numbers.isEmpty then return "NaN" mean = 1 number = Rexx loop number over numbers mean = mean * number end return Math.pow(mean, 1 / numbers.size) -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ method harmonicMean(numbers = java.util.List) public static returns Rexx -- somewhat arbitrary return for ooRexx if numbers.isEmpty then return "NaN" mean = 0 number = Rexx loop number over numbers if number = 0 then return "Nan" mean = mean + (1 / number) end -- problem here... return numbers.size / mean  {{out}}  Arithmetic = 5.5, Geometric = 4.528728688116765, Harmonic = 3.4141715214740550062  ## Nim import math, sequtils, future proc amean(num: seq[float]): float = sum(num) / float(len(num)) proc gmean(num: seq[float]): float = result = 1 for n in num: result *= n result = pow(result, 1.0 / float(num.len)) proc hmean(num: seq[float]): float = for n in num: result += 1.0 / n result = float(num.len) / result proc ameanFunctional(num: seq[float]): float = sum(num) / float(num.len) proc gmeanFunctional(num: seq[float]): float = num.foldl(a * b).pow(1.0 / float(num.len)) proc hmeanFunctional(num: seq[float]): float = float(num.len) / sum(num.mapIt(float, 1.0 / it)) let numbers = toSeq(1..10).map((x: int) => float(x)) echo amean(numbers), " ", gmean(numbers), " ", hmean(numbers)  {{out}} 5.5000000000000000e+00 4.5287286881167654e+00 3.4141715214740551e+00  =={{header|Oberon-2}}== Oxford Oberon-2  MODULE PythMean; IMPORT Out, ML := MathL; PROCEDURE Triplets(a: ARRAY OF INTEGER;VAR triplet: ARRAY OF LONGREAL); VAR i: INTEGER; BEGIN triplet[0] := 0.0;triplet[1] := 0.0; triplet[2] := 0.0; FOR i:= 0 TO LEN(a) - 1 DO triplet[0] := triplet[0] + a[i]; triplet[1] := triplet[1] + ML.Ln(a[i]); triplet[2] := triplet[2] + (1 / a[i]) END END Triplets; PROCEDURE Means*(a: ARRAY OF INTEGER); VAR triplet: ARRAY 3 OF LONGREAL; BEGIN Triplets(a,triplet); Out.String("A(1 .. 10): ");Out.LongReal(triplet[0] / LEN(a));Out.Ln; Out.String("G(1 .. 10): ");Out.LongReal(ML.Exp(triplet[1]/ LEN(a)));Out.Ln; Out.String("H(1 .. 10): ");Out.LongReal(LEN(a) / triplet[2]);Out.Ln; END Means; VAR nums: ARRAY 10 OF INTEGER; i: INTEGER; BEGIN FOR i := 0 TO LEN(nums) - 1 DO nums[i] := i + 1 END; Means(nums) END PythMean.  {{out}}  A(1 .. 10): 5.50000000000 G(1 .. 10): 4.52872868812 H(1 .. 10): 3.41417152147  ## Objeck {{trans|Java}} class PythagMeans { function : Main(args : String[]) ~ Nil { array := [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0]; arithmetic := ArithmeticMean(array); geometric := GeometricMean(array); harmonic := HarmonicMean(array); arith_geo := arithmetic >= geometric; geo_harm := geometric >= harmonic; "A = {$arithmetic}, G = {$geometric}, H = {$harmonic}"->PrintLine();
"A >= G is {$arith_geo}, G >= H is {$geo_harm}"->PrintLine();
}

function : native : ArithmeticMean(numbers : Float[]) ~ Float {
if(numbers->Size() = 0) { return -1.0; };

mean := 0.0;
each(i : numbers) {
mean += numbers[i];
};

return mean / numbers->Size();
}

function : native : GeometricMean(numbers : Float[]) ~ Float {
if(numbers->Size() = 0) { return -1.0; };

mean := 1.0;
each(i : numbers) {
mean *= numbers[i];
};

return mean->Power(1.0 / numbers->Size());
}

function : native : HarmonicMean(numbers : Float[]) ~ Float {
if(numbers->Size() = 0) { return -1.0; };

mean := 0.0;
each(i : numbers) {
mean += (1.0 / numbers[i]);
};

return numbers->Size() / mean;
}
}


Output:


A = 5.500, G = 4.529, H = 3.414
A >= G is true, G >= H is true



## OCaml

The three means in one function

let means v =
let n = Array.length v
and a = ref 0.0
and b = ref 1.0
and c = ref 0.0 in
for i=0 to n-1 do
a := !a +. v.(i);
b := !b *. v.(i);
c := !c +. 1.0/.v.(i);
done;
let nn = float_of_int n in
(!a /. nn, !b ** (1.0/.nn), nn /. !c)
;;


{{out}}

means (Array.init 10 (function i -> (float_of_int (i+1)))) ;;
(* (5.5, 4.5287286881167654, 3.4141715214740551) *)


Another implementation using [http://caml.inria.fr/pub/docs/manual-ocaml/libref/Array.html#VALfold_left Array.fold_left] instead of a '''for''' loop:

let means v =
let (a, b, c) =
Array.fold_left
(fun (a, b, c) x -> (a+.x, b*.x, c+.1./.x))
(0.,1.,0.) v
in
let n = float_of_int (Array.length v) in
(a /. n, b ** (1./.n), n /. c)
;;


## Octave


A = mean(list);     % arithmetic mean
G = mean(list,'g'); % geometric mean
H = mean(list,'a'); % harmonic mean



## Oforth

import: mapping

: A ( x )
x sum
x size dup ifZero: [ 2drop null ] else: [ >float / ]
;

: G( x )   #* x reduce  x size inv powf ;

: H( x )   x size x map( #inv ) sum / ;

: averages
| g |
"Geometric mean  :" . 10 seq G dup .cr ->g
"Arithmetic mean :" . 10 seq A dup . g >= ifTrue: [ " ==> A >= G" .cr ]
"Harmonic mean   :" . 10 seq H dup . g <= ifTrue: [ " ==> G >= H" .cr ]
;


{{out}}


Geometric mean  : 4.52872868811677
Arithmetic mean : 5.5 ==> A >= G
Harmonic mean   : 3.41417152147406 ==> G >= H



## ooRexx

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


{{out}}

Arithmetic = 5.5, Geometric = 4.52872869, Harmonic = 3.41417153


## Oz

declare
%% helpers
fun {Sum Xs} {FoldL Xs Number.'+' 0.0} end
fun {Product Xs} {FoldL Xs Number.'*' 1.0} end
fun {Len Xs} {Int.toFloat {Length Xs}} end

fun {AMean Xs}
{Sum Xs}
/
{Len Xs}
end

fun {GMean Xs}
{Pow
{Product Xs}
1.0/{Len Xs}}
end

fun {HMean Xs}
{Len Xs}
/
{Sum {Map Xs fun {$X} 1.0 / X end}} end Numbers = {Map {List.number 1 10 1} Int.toFloat} [A G H] = [{AMean Numbers} {GMean Numbers} {HMean Numbers}] in {Show [A G H]} A >= G = true G >= H = true  ## PARI/GP General implementations: arithmetic(v)={ sum(i=1,#v,v[i])/#v }; geometric(v)={ prod(i=1,#v,v[i])^(1/#v) }; harmonic(v)={ #v/sum(i=1,#v,1/v[i]) }; v=vector(10,i,i); [arithmetic(v),geometric(v),harmonic(v)]  Specific to the first ''n'' positive integers: arithmetic_first(n)={ (n+1)/2 }; geometric_first(n)={ n!^(1/n) }; harmonic_first(n)={ n/if(n>1000, log(n)+Euler+1/(n+n)+1/(12*n^2)-1/(120*n^4)+1/(252*n^6)-1/(240*n^8)+1/(132*n^10) , n/sum(k=1,n,1/k) ) }; [arithmetic_first(10),geometric_first(10),harmonic_first(10)] %[1]>=%[2] && %[2] >= %[3]  These are, asymptotically, n/2, n/e, and n/log n. ## Pascal See [[Averages/Pythagorean_means&#Delphi | Delphi]] ## Perl sub A { my$a = 0;
$a +=$_ for @_;
return $a / @_; } sub G { my$p = 1;
$p *=$_ for @_;
return  $p**(1/@_); # power of 1/n == root of n } sub H { my$h = 0;
$h += 1/$_ for @_;
return @_/$h; } my @ints = (1..10); my$a = A(@ints);
my $g = G(@ints); my$h = H(@ints);

print "A=$a\nG=$g\nH=$h\n"; die "Error" unless$a >= $g and$g >= $h;  ## Perl 6 {{works with|Rakudo|2015.12}} sub A { ([+] @_) / @_ } sub G { ([*] @_) ** (1 / @_) } sub H { @_ / [+] 1 X/ @_ } say "A(1,...,10) = ", A(1..10); say "G(1,...,10) = ", G(1..10); say "H(1,...,10) = ", H(1..10);  {{out}} A(1,...,10) = 5.5 G(1,...,10) = 4.52872868811677 H(1,...,10) = 3.41417152147406  ## Phix (note to self: iff should really be a builtin) function arithmetic_mean(sequence s) return sum(s)/length(s) end function function geometric_mean(sequence s) atom p = 1 for i=1 to length(s) do p *= s[i] end for return power(p,1/length(s)) end function function harmonic_mean(sequence s) atom rsum = 0 for i=1 to length(s) do rsum += 1/s[i] end for return length(s)/rsum end function function iff(integer condition, object Tval, object Fval) if condition then return Tval else return Fval end if end function constant s = {1,2,3,4,5,6,7,8,9,10} constant arithmetic = arithmetic_mean(s), geometric = geometric_mean(s), harmonic = harmonic_mean(s) printf(1,"Arithmetic: %.10g\n", arithmetic) printf(1,"Geometric: %.10g\n", geometric) printf(1,"Harmonic: %.10g\n", harmonic) printf(1,"Arithmetic>=Geometric>=Harmonic: %s\n", {iff((arithmetic>=geometric and geometric>=harmonic),"true","false")})  {{out}}  Arithmetic: 5.5 Geometric: 4.528728688 Harmonic: 3.414171521 Arithmetic>=Geometric>=Harmonic: true  ## PHP <?php // Created with PHP 7.0 function ArithmeticMean(array$values)
{
return array_sum($values) / count($values);
}

function GeometricMean(array $values) { return array_product($values) ** (1 / count($values)); } function HarmonicMean(array$values)
{
$sum = 0; foreach ($values as $value) {$sum += 1 / $value; } return count($values) / $sum; }$values = array(1, 2, 3, 4, 5, 6, 7, 8, 9, 10);

echo "Arithmetic: " . ArithmeticMean($values) . "\n"; echo "Geometric: " . GeometricMean($values) . "\n";
echo "Harmonic: " . HarmonicMean($values) . "\n";  {{out}}  Arithmetic: 5.5 Geometric: 4.5287286881168 Harmonic: 3.4141715214741  ## PicoLisp (load "@lib/math.l") (let (Lst (1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0) Len (length Lst)) (prinl "Arithmetic mean: " (format (/ (apply + Lst) Len) *Scl ) ) (prinl "Geometric mean: " (format (pow (*/ (apply * Lst) (** 1.0 (dec Len))) (/ 1.0 Len)) *Scl ) ) (prinl "Harmonic mean: " (format (*/ (* 1.0 Len) 1.0 (sum '((N) (*/ 1.0 1.0 N)) Lst)) *Scl ) ) )  {{out}} Arithmetic mean: 5.500000 Geometric mean: 4.528729 Harmonic mean: 3.414172  ## PL/I  declare n fixed binary, (Average, Geometric, Harmonic) float; declare A(10) float static initial (1,2,3,4,5,6,7,8,9,10); n = hbound(A,1); /* compute the average */ Average = sum(A)/n; /* Compute the geometric mean: */ Geometric = prod(A)**(1/n); /* Compute the Harmonic mean: */ Harmonic = n / sum(1/A); put skip data (Average); put skip data (Geometric); put skip data (Harmonic); if Average < Geometric then put skip list ('Error'); if Geometric < Harmonic then put skip list ('Error');  Results:  AVERAGE= 5.50000E+0000; GEOMETRIC= 4.52873E+0000; HARMONIC= 3.41417E+0000;  ## PostScript /pythamean{ /x exch def /sum 0 def /prod 1 def /invsum 0 def /i 1 def x{ /sum sum i add def /prod prod i mul def /invsum invsum i -1 exp add def /i i 1 add def }repeat (Arithmetic Mean : ) print sum x div = (Geometric Mean : ) print prod x -1 exp exp = (Harmonic Mean : ) print x invsum div = }def 10 pythamean  {{out}} txt Arithmetic Mean : 5.5 Geometric Mean : 4.52873 Harmonic Mean : 3.41417  {{libheader|initlib}}  /numbers {[1 10] 1 range}. /recip {1 exch div}. % Arithmetic mean numbers dup 0 {+} fold exch length div % Geometric mean numbers dup 1 {*} fold exch length recip exp % Harmonic mean numbers dup 0 {recip +} fold exch length exch div  ## PowerShell $A = 0
$LogG = 0$InvH = 0

$ii = 1..10 foreach($i in $ii) { # Arithmetic mean is computed directly$A += $i /$ii.Count
# Geometric mean is computed using Logarithms
$LogG += [Math]::Log($i) / $ii.Count # Harmonic mean is computed using its inverse$InvH += 1 / ($i *$ii.Count)
}

$G = [Math]::Exp($LogG)
$H = 1/$InvH

write-host "Arithmetic mean: A = $A" write-host "Geometric mean: G =$G"
write-host "Harmonic mean:   H = $H" write-host "Is A >= G ?$($A -ge$G)"
write-host "Is G >= H ? $($G -ge $H)"  {{out}} Arithmetic mean: A = 5.5 Geometric mean: G = 4.52872868811676 Harmonic mean: H = 3.41417152147405 Is A >= G ? True Is G >= H ? True  ## PureBasic Procedure.d ArithmeticMean() For a = 1 To 10 mean + a Next ProcedureReturn mean / 10 EndProcedure Procedure.d GeometricMean() mean = 1 For a = 1 To 10 mean * a Next ProcedureReturn Pow(mean, 1 / 10) EndProcedure Procedure.d HarmonicMean() For a = 1 To 10 mean.d + 1 / a Next ProcedureReturn 10 / mean EndProcedure If HarmonicMean() <= GeometricMean() And GeometricMean() <= ArithmeticMean() Debug "true" EndIf Debug ArithmeticMean() Debug GeometricMean() Debug HarmonicMean()  ## Python {{works with|Python|3}} from operator import mul from functools import reduce def amean(num): return sum(num) / len(num) def gmean(num): return reduce(mul, num, 1)**(1 / len(num)) def hmean(num): return len(num) / sum(1 / n for n in num) numbers = range(1, 11) # 1..10 a, g, h = amean(numbers), gmean(numbers), hmean(numbers) print(a, g, h) assert a >= g >= h  {{out}} 5.5 4.52872868812 3.41417152147  These are the same in Python 2 apart from requiring explicit float division (either through float() casts or float literals such as 1./n); or better, do a from future import division, which works on Python 2.2+ as well as Python 3, and makes division work consistently like it does in Python 3. ## R Initialise x  x <- 1:10  Arithmetic mean  a <- sum(x)/length(x)  or  a <- mean(x)  The geometric mean  g <- prod(x)^(1/length(x))  The harmonic mean (no error checking that $x_i\ne 0,\text\left\{ \right\} \forall \text\left\{ \right\}i=1\ldots n$)  h <- length(x)/sum(1/x)  Then:  a > g  and  g > h  give both [1] TRUE  ## Racket  #lang racket (define (arithmetic xs) (/ (for/sum ([x xs]) x) (length xs))) (define (geometric xs) (expt (for/product ([x xs]) x) (/ (length xs)))) (define (harmonic xs) (/ (length xs) (for/sum ([x xs]) (/ x)))) (define xs (range 1 11)) (arithmetic xs) (geometric xs) (harmonic xs) (>= (arithmetic xs) (geometric xs) (harmonic xs))  {{out}}  5 1/2 4.528728688116765 3 3057/7381 #t  ## REXX REXX doesn't have a '''POW''' function, so an '''IROOT''' ('''i'''nteger '''root''') function is included here; it includes an extra error check if used as a general purpose function that would otherwise yield a complex result. /*REXX program computes and displays the Pythagorean means [Amean, Gmean, Hmean]. */ numeric digits 20 /*use a little extra for the precision.*/ parse arg n . /*obtain the optional argument from CL.*/ if n=='' | n=="," then n=10 /*None specified? Then use the default*/ sum=0; prod=1; rSum=0 /*initialize sum/product/reciprocal sum*/$=;                     do #=1  for n;   $=$ #   /*generate list by appending # to list.*/
sum = sum   +    #       /*compute the sum of all the elements. */
prod= prod  *    #       /*compute the product of all elements. */
rSum= rSum  +  1/#       /*compute the sum of the reciprocals.  */
end   /*#*/
say ' list ='$/*display the list of numbers used. */ say 'Amean =' sum / n /*calculate & display arithmetic mean.*/ say 'Gmean =' Iroot(prod, n) /* " " " geometric " */ say 'Hmean =' n / rSum /* " " " harmonic " */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ Iroot: procedure; arg x 1 ox, y 1 oy /*get both args, and also a copy of X&Y*/ if x=0 | x=1 | y=1 then return x /*handle special case of zero and unity*/ if y=0 then return 1 /* " " " " a zero root.*/ if x<0 & y//2==0 then return IrootErr() x=abs(x); y=abs(y); m=y - 1 /*use the absolute value for X and Y. */ oDigs=digits(); a=oDigs + 5 /*save original digits; add five digs.*/ g=(x+1) / y**y /*use this as the first guesstimate. */ d=5 /*start with 5 dec digs, saves CPU time*/ do until d==a /*keep going as digits are increased. */ d=min(d+d, a); numeric digits d; f=d-2 /*limit digits to original digits + 5.*/ og= /*use a non-guess for the old G (guess)*/ do forever; gm=g**m /*keep computing at the Yth root. */ _=format( (m*g*gm + x) / (y*gm), , f) /*this is the nitty─gritty calculation.*/ if _=g | _=og then leave /*are we close enough yet? */ og=g; g=_ /*save guess ──► OG; set the new guess.*/ end /*forever*/ end /*until */ if oy<0 then g=1/g /*use reciprocal when Y is negative. */ numeric digits oDigs; return sign(ox)*g/1 /*normalize to original decimal digits.*/ /*──────────────────────────────────────────────────────────────────────────────────────*/ IrootErr: say '***error*** (from Iroot): root' y "can't be even if 1st argument is < 0." return '[n/a]' /*return a "not applicable" string. */  '''output''' using the default inputs:  list = 1 2 3 4 5 6 7 8 9 10 Amean = 5.5 Gmean = 4.5287286881167647622 Hmean = 3.4141715214740550062  ## Ring  decimals(8) array = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] see "arithmetic mean = " + arithmeticMean(array) + nl see "geometric mean = " + geometricMean(array) + nl see "harmonic mean = " + harmonicMean(array) + nl func arithmeticMean a return summary(a) / len(a) func geometricMean a b = 1 for i = 1 to len(a) b *= a[i] next return pow(b, (1/len(a))) func harmonicMean a b = list(len(a)) for nr = 1 to len(a) b[nr] = 1/a[nr] next return len(a) / summary(b) func summary s sum = 0 for n = 1 to len(s) sum += s[n] next return sum  Output:  arithmetic mean = 5.50000000 geometric mean = 4.52872869 harmonic mean = 3.41417152  ## Ruby {{works with|Ruby|1.9+}} class Array def arithmetic_mean inject(0.0, :+) / length end def geometric_mean inject(:*) ** (1.0 / length) end def harmonic_mean length / inject(0.0) {|s, m| s + 1.0/m} end end class Range def method_missing(m, *args) case m when /_mean$/ then to_a.send(m)
else super
end
end
end

p a = (1..10).arithmetic_mean
p g = (1..10).geometric_mean
p h = (1..10).harmonic_mean
# is h < g < a ??
p g.between?(h, a)


{{out}}


5.5
4.528728688116765
3.414171521474055
true



## Run BASIC

bXsum   = 1
for i   = 1 to 10
sum   = sum + i                ' sum of 1 -> 10
bXsum = bXsum * i              ' sum i * i
sum1i = sum1i + (1/i)          ' sum 1/i
next

average   = sum / 10
geometric = bXsum ^ (1/10)
harmonic  = 10/sum1i

print "ArithmeticMean:";average
print "Geometric Mean:";geometric
print " Harmonic Mean:";harmonic

if (average >= geometric) and (geometric >= harmonic) then print "True" else print "False"


{{out}}


Arithmetic Mean:5.5
Geometric Mean:4.52872869
Harmonic Mean:3.41417132
True


## Rust

fn main() {
let mut sum = 0.0;
let mut prod = 1;
let mut recsum = 0.0;
for i in 1..11{
sum += i as f32;
prod *= i;
recsum += 1.0/(i as f32);
}
let avg = sum/10.0;
let gmean = (prod as f32).powf(0.1);
let hmean = 10.0/recsum;
println!("Average: {}, Geometric mean: {}, Harmonic mean: {}", avg, gmean, hmean);
assert!( ( (avg >= gmean) && (gmean >= hmean) ), "Incorrect calculation");

}



{{out}}


Average: 5.5, Geometric mean:4.528729, Harmonic mean: 3.4141712



## Scala

{{works with|Scala|2.8+}}

def arithmeticMean(n: Seq[Int]) = n.sum / n.size.toDouble
def geometricMean(n: Seq[Int])  = math.pow(n.foldLeft(1.0)(_*_), 1.0 / n.size.toDouble)
def harmonicMean(n: Seq[Int])   = n.size / n.map(1.0 / _).sum

var nums = 1 to 10
var a = arithmeticMean(nums)
var g = geometricMean(nums)
var h = harmonicMean(nums)

println("Arithmetic mean " + a)
println("Geometric mean  " + g)
println("Harmonic mean   " + h)

assert(a >= g && g >= h)


{{out}}

Arithmetic mean 5.5
Geometric mean  4.528728688116765
Harmonic mean   3.414171521474055


## Scheme

{{Works with|Scheme|R$^5$RS}}

(define (a-mean l)
(/ (apply + l) (length l)))

(define (g-mean l)
(expt (apply * l) (/ (length l))))

(define (h-mean l)
(/ (length l) (apply + (map / l))))

(define (iota start stop)
(if (> start stop)
(list)
(cons start (iota (+ start 1) stop))))

(let* ((l (iota 1 10)) (a (a-mean l)) (g (g-mean l)) (h (h-mean l)))
(display a)
(display " >= ")
(display g)
(display " >= ")
(display h)
(newline)
(display (>= a g h))
(newline))


{{out}} 11/2 >= 4.528728688116765 >= 25200/7381 #t



## Seed7

seed7
$include "seed7_05.s7i"; include "float.s7i"; const array float: numbers is [] (1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0); const func proc: main is func local var float: number is 0.0; var float: sum is 0.0; var float: product is 1.0; var float: reciprocalSum is 0.0; begin for number range numbers do sum +:= number; product *:= number; reciprocalSum +:= 1.0 / number; end for; writeln("Arithmetic mean: " <& sum / flt(length(numbers))); writeln("Geometric mean: " <& product ** (1.0 / flt(length(numbers)))); writeln("Harmonic mean: " <& flt(length(numbers)) / reciprocalSum); end func;  {{out}}  Arithmetic mean: 5.5 Geometric mean: 4.528728961944580078125 Harmonic mean: 3.4141712188720703125  ## Sidef func A(a) { a.sum / a.len } func G(a) { a.prod.root(a.len) } func H(a) { a.len / a.map{1/_}.sum }  The same thing, using hyper-operators: func A(a) { a«+» / a.len } func G(a) { a«*» ** (1/a.len) } func H(a) { a.len / (a«/«1 «+») }  Calling the functions: say("A(1,...,10) = ", A(1..10)); say("G(1,...,10) = ", G(1..10)); say("H(1,...,10) = ", H(1..10));  {{out}} A(1,...,10) = 5.5 G(1,...,10) = 4.528728688116764762203309337195508793499 H(1,...,10) = 3.414171521474055006096734859775098225173  ## SQL It may not be possible to calculate a geometric mean in a query, but the other two are easy enough.  --setup create table averages (val integer); insert into averages values (1); insert into averages values (2); insert into averages values (3); insert into averages values (4); insert into averages values (5); insert into averages values (6); insert into averages values (7); insert into averages values (8); insert into averages values (9); insert into averages values (10); -- calculate means select 1/avg(1/val) as harm, avg(val) as arith from averages;  {{out}}  HARM ARITH ---------- ---------- 3.41417152 5.5  ## Smalltalk {{works with|GNU Smalltalk}} This extends the class Collection, so these three methods can be called over any kind of collection, it is enough the the objects of the collection understand +, *, raisedTo, reciprocal and /. Collection extend [ arithmeticMean [ ^ (self fold: [:a :b| a + b ]) / (self size) ] geometricMean [ ^ (self fold: [:a :b| a * b]) raisedTo: (self size reciprocal) ] harmonicMean [ ^ (self size) / ((self collect: [:x|x reciprocal]) fold: [:a :b| a + b ] ) ] ] |a| a := #(1 2 3 4 5 6 7 8 9 10). a arithmeticMean asFloat displayNl. a geometricMean asFloat displayNl. a harmonicMean asFloat displayNl. ((a arithmeticMean) >= (a geometricMean)) displayNl. ((a geometricMean) >= (a harmonicMean)) displayNl.  {{out}} 5.5 4.528728688116765 3.414171521474055 true true  ## Stata The command [http://www.stata.com/help.cgi?ameans ameans] prints the arithmetic, geometric and harmonic means, together with confidence intervals. clear all set obs 10 gen x=_n ameans x Variable | Type Obs Mean [95% Conf. Interval]  ## -------------+--------------------------------------------------------------- x | Arithmetic 10 5.5 3.334149 7.665851 | Geometric 10 4.528729 2.680672 7.650836 | Harmonic 10 3.414172 2.035664 10.57602  ## Tcl tcl proc arithmeticMean list { set sum 0.0 foreach value$list { set sum [expr {$sum +$value}] }
return [expr {$sum / [llength$list]}]
}
proc geometricMean list {
set product 1.0
foreach value $list { set product [expr {$product * $value}] } return [expr {$product ** (1.0/[llength $list])}] } proc harmonicMean list { set sum 0.0 foreach value$list { set sum [expr {$sum + 1.0/$value}] }
return [expr {[llength $list] /$sum}]
}

set nums {1 2 3 4 5 6 7 8 9 10}
set A10 [arithmeticMean $nums] set G10 [geometricMean$nums]
set H10 [harmonicMean $nums] puts "A10=$A10, G10=$G10, H10=$H10"
if {$A10 >=$G10} { puts "A10 >= G10" }
if {$G10 >=$H10} { puts "G10 >= H10" }


{{out}}


A10=5.5, G10=4.528728688116765, H10=3.414171521474055
A10 >= G10
G10 >= H10



## Ursala

#import std
#import flo

data = ari10(1.,10.)   # arithmetic progression, length 10 with endpoints 1 and 10

a = mean data
g = exp mean ln* data
h = div/1. mean div/*1. data

#cast %eLbX

main = ^(~&,ordered not fleq) <a,g,h>


{{out}}

(
<5.500000e+00,4.528729e+00,3.414172e+00>,
true)


## Vala

Most valac setups will need "-X -lm" added to the compile command to include the C math library.


double arithmetic(int[] list){
double mean;
double sum = 0;
foreach(int number in list){
sum += number;
} // foreach

mean = sum / list.length;

return mean;
} // end arithmetic mean

double geometric(int[] list){
double mean;
double product = 1;
foreach(int number in list){
product *= number;
} // foreach

mean = Math.pow(product, (1 / (double) list.length));

return mean;
} // end geometric mean

double harmonic(int[] list){
double mean;
double sum_inverse = 0;
foreach(int number in list){
sum_inverse += (1 / (double) number);
} // foreach

mean = (double) list.length / sum_inverse;

return mean;
} // end harmonic mean

public static void main(){
int[] list = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};

double arithmetic_mean = arithmetic(list);
double geometric_mean = geometric(list);
double harmonic_mean = harmonic(list);

// should be 5.5
stdout.printf("Arithmetic mean: %s\n", arithmetic_mean.to_string());

// should be 4.528728688116765
stdout.printf("Geometric mean: %s\n", geometric_mean.to_string());

// should be 4.528728688116765
stdout.printf("Harmonic mean: %s\n", harmonic_mean.to_string());
}



{{out}}


Arithmetic mean: 5.5
Geometric mean: 4.5287286881167654
Harmonic mean: 3.4141715214740551



## VBA

Uses Excel VBA.

Private Function arithmetic_mean(s() As Variant) As Double
arithmetic_mean = WorksheetFunction.Average(s)
End Function
Private Function geometric_mean(s() As Variant) As Double
geometric_mean = WorksheetFunction.GeoMean(s)
End Function
Private Function harmonic_mean(s() As Variant) As Double
harmonic_mean = WorksheetFunction.HarMean(s)
End Function
Public Sub pythagorean_means()
Dim s() As Variant
s = [{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}]
Debug.Print "A ="; arithmetic_mean(s)
Debug.Print "G ="; geometric_mean(s)
Debug.Print "H ="; harmonic_mean(s)
End Sub


{{out}}

A = 5,5
G = 4,52872868811677
H = 3,41417152147406


## VBScript


Function arithmetic_mean(arr)
sum = 0
For i = 0 To UBound(arr)
sum = sum + arr(i)
Next
arithmetic_mean = sum / (UBound(arr)+1)
End Function

Function geometric_mean(arr)
product = 1
For i = 0 To UBound(arr)
product = product * arr(i)
Next
geometric_mean = product ^ (1/(UBound(arr)+1))
End Function

Function harmonic_mean(arr)
sum = 0
For i = 0 To UBound(arr)
sum = sum + (1/arr(i))
Next
harmonic_mean = (UBound(arr)+1) / sum
End Function

WScript.StdOut.WriteLine arithmetic_mean(Array(1,2,3,4,5,6,7,8,9,10))
WScript.StdOut.WriteLine geometric_mean(Array(1,2,3,4,5,6,7,8,9,10))
WScript.StdOut.WriteLine harmonic_mean(Array(1,2,3,4,5,6,7,8,9,10))



{{Out}}


5.5
4.52872868811677
3.41417152147406



## Visual Basic .NET

{{trans|C#}}

Imports System.Runtime.CompilerServices

Module Module1

<Extension()>
Function Gmean(n As IEnumerable(Of Double)) As Double
Return Math.Pow(n.Aggregate(Function(s, i) s * i), 1.0 / n.Count())
End Function

<Extension()>
Function Hmean(n As IEnumerable(Of Double)) As Double
Return n.Count() / n.Sum(Function(i) 1.0 / i)
End Function

Sub Main()
Dim nums = From n In Enumerable.Range(1, 10) Select CDbl(n)

Dim a = nums.Average()
Dim g = nums.Gmean()
Dim h = nums.Hmean()

Console.WriteLine("Arithmetic mean {0}", a)
Console.WriteLine(" Geometric mean {0}", g)
Console.WriteLine("  Harmonic mean {0}", h)
Debug.Assert(a >= g AndAlso g >= h)
End Sub

End Module


{{out}}

Arithmetic mean 5.5
Geometric mean 4.52872868811677
Harmonic mean 3.41417152147406


## XPL0

include c:\cxpl\codes;

func real Power(X, Y);          \X raised to the Y power
real X, Y;                      \ (from StdLib.xpl)
return Exp(Y * Ln(X));

int  N, Order;
real R, A, A1, G, G1, H, H1;
[A1:= 0.0;  G1:= 1.0;  H1:= 0.0;
Order:= true;
for N:= 1 to 10 do
[R:= float(N);          \convert integer N to real R
A1:= A1 + R;
A:= A1/R;               \arithmetic mean
G1:= G1 * R;
G:= Power(G1, 1.0/R);   \geometric mean (Nth root of G1)
if G>A then Order:= false;
H1:= H1 + 1.0/R;
H:= R/H1;               \harmonic mean
if H>G then Order:= false;
];
RlOut(0, A); CrLf(0);
RlOut(0, G); CrLf(0);
RlOut(0, H); CrLf(0);
if not Order then Text(0, "NOT ");
Text(0, "ALWAYS DECREASING ORDER
");
]


{{out}}


5.50000
4.52873
3.41417
ALWAYS DECREASING ORDER



## zkl

ns:=T(1,2,3,4,5,6,7,8,9,10);
ns.sum(0.0)/ns.len();					   // Arithmetic mean
ns.reduce('*,1.0).pow(1.0/ns.len());			   // Geometric mean
ns.len().toFloat() / ns.reduce(fcn(p,n){ p + 1.0/n },0.0); // Harmonic mean


{{out}}


5.5
4.52873
3.41417



[[Category:Geometry]]