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Averages/Pythagorean means: Difference between revisions
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[[Category:Geometry]]
{{task}}
;Task
Compute all three of the [[wp:Pythagorean means|Pythagorean means]] of the set of integers <big>1</big> through <big>10</big> (inclusive).
Show that <big><math>A(x_1,\ldots,x_n) \geq G(x_1,\ldots,x_n) \geq H(x_1,\ldots,x_n)</math></big> for this set of positive integers.
* The most common of the three means, the [[
: <big><math>
* The [[wp:Geometric mean|geometric mean]] is the <math>n</math>th root of the product of the list:
: <big><math> G(x_1, \ldots, x_n) = \sqrt[n]{x_1 \cdots x_n} </math></big>
* The [[wp:Harmonic mean|harmonic mean]] is <math>n</math> divided by the sum of the reciprocal of each item in the list:
: <big><math> H(x_1, \ldots, x_n) = \frac{n}{\frac{1}{x_1} + \cdots + \frac{1}{x_n}} </math></big>
{{task heading|See also}}
{{Related tasks/Statistical measures}}
<br><hr>
=={{header|11l}}==
<syntaxhighlight lang="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))</syntaxhighlight>
{{out}}
<pre>
5.5
4.52873
3.41417
</pre>
=={{header|Action!}}==
{{libheader|Action! Tool Kit}}
<syntaxhighlight lang="action!">INCLUDE "D2:REAL.ACT" ;from the Action! Tool Kit
PROC InverseI(INT a,result)
REAL one,x
IntToReal(1,one)
IntToReal(a,x)
RealDiv(one,x,result)
RETURN
PROC ArithmeticMean(INT ARRAY a INT count REAL POINTER result)
INT i
REAL x,sum,tmp
IntToReal(0,sum)
FOR i=0 TO count-1
DO
IntToReal(a(i),x)
RealAdd(sum,x,tmp)
RealAssign(tmp,sum)
OD
IntToReal(count,tmp)
RealDiv(sum,tmp,result)
RETURN
PROC GeometricMean(INT ARRAY a INT count REAL POINTER result)
INT i
REAL x,prod,tmp
IntToReal(1,prod)
FOR i=0 TO count-1
DO
IntToReal(a(i),x)
RealMult(prod,x,tmp)
RealAssign(tmp,prod)
OD
InverseI(count,tmp)
Power(prod,tmp,result)
RETURN
PROC HarmonicMean(INT ARRAY a INT count REAL POINTER result)
INT i
REAL x,sum,tmp
IntToReal(0,sum)
FOR i=0 TO count-1
DO
InverseI(a(i),x)
RealAdd(sum,x,tmp)
RealAssign(tmp,sum)
OD
IntToReal(count,tmp)
RealDiv(tmp,sum,result)
RETURN
PROC Main()
BYTE i
INT ARRAY a=[1 2 3 4 5 6 7 8 9 10]
REAL result
Put(125) PutE() ;clear screen
ArithmeticMean(a,10,result)
Print("Arithmetic mean=") PrintRE(result)
GeometricMean(a,10,result)
Print(" Geometric mean=") PrintRE(result)
HarmonicMean(a,10,result)
Print(" Harmonic mean=") PrintRE(result)
RETURN</syntaxhighlight>
{{out}}
[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Pythagorean_means.png Screenshot from Atari 8-bit computer]
<pre>
Arithmetic mean=5.5
Geometric mean=4.52872861
Harmonic mean=3.41417153
</pre>
=={{header|ActionScript}}==
<syntaxhighlight lang="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));</syntaxhighlight>
=={{header|Ada}}==
pythagorean_means.ads:
<syntaxhighlight lang="ada">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;</syntaxhighlight>
pythagorean_means.adb:
<syntaxhighlight lang="ada">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;</syntaxhighlight>
example main.adb:
<syntaxhighlight lang="ada">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;</syntaxhighlight>
=={{header|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}}
<syntaxhighlight lang="algol68">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))
)</syntaxhighlight>
Lunix command:
a68g Averages_Pythagorean_means.a68 - 1 2 3 4 5 6 7 8 9 10
{{out}}
<pre>
c: 10.0000
s: 55.0000
p: 3628800.0000
r: 2.9290
Arithmetic mean = 5.5000
Geometric mean = 4.5287
Harmonic mean = 3.4142
</pre>
=={{header|ALGOL W}}==
<syntaxhighlight lang="algolw">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.</syntaxhighlight>
{{out}}
<pre>
Arithmetic mean: 5.50000
Geometric mean: 4.52872
Harmonic mean: 3.41417
</pre>
=={{header|Amazing Hopper}}==
Think about "talk" programming...
<syntaxhighlight lang="amazing hopper">
#include <hopper.h>
/* An example of definitions in pseudo-natural language, with synonimous.
These definitions can be inside a definition file (xxxx.h) */
#define getasinglelistof(_X_) {_X_},
#synon getasinglelistof getalistof
#define integerrandomnumbers _V1000_=-1,rand array(_V1000_),mulby(10),ceil,
#define randomnumbers _V1000_=-1,rand array(_V1000_)
#define rememberitin(_X_) _X_=0,cpy(_X_)
#synon rememberitin rememberthisnumbersin
#define rememberas(_X_) mov(_X_)
#define remember(_X_) {_X_}
//#synon remember with ---> this exist in HOPPER.H
#defn nowconsiderthis(_X_) #ATOM#CMPLX,print
#synon nowconsiderthis nowconsider,considerthis,consider,nowputtext,puttext,andprint
#define andprintwithanewline {"\n"}print
#synon andprintwithanewline printwithanewline
//#defn andprint(_X_) #ATOM#CMPLX,print
#define putanewline {"\n"}
#define withanewline "\n"
#define andprintit print
#synon andprintit printit,andprint
#define showit show
#define afterdoingit emptystack?,not,do{ {"I cannot continue due to retentive data "},throw(1001) }
#synon afterdoingit secondly,finally
#define then emptystack?do{ {"I cannot continue because data is missing "},throw(1000) }
/* why "#context" and not "#define"?
becose "#context" need a value in the stack for continue.
Internally, "domeanit" tranform to "gosub(calculatearithmeticmean)",
and "gosub" works only if it finds a data in the stack */
#context calculatethegeometricmean
#synon calculatethegeometricmean calculategeometricmean,getgeometricmean
#context calculatetheharmonicmean
#synon calculatetheharmonicmean calculateharmonicmean,getharmonicmean
#context calculatearitmethicmean
#synon calculatearitmethicmean calculatesinglemean,calculatemean,domeanit
main:
consider this ("Arithmetic Mean: ")
get a list of '10,10' integer random numbers; remember this numbers in 'list of numbers';
then, do mean it, and print with a new line.
after doing it, consider ("Geometric Mean: "), remember 'list of numbers', calculate the geometric mean;
then, put a new line, and print it.
/*
Okay. This can be a bit long, if we have to write the program;
But what if we just had to talk, and the language interpreter takes care of the rest?
*/
secondly, now consider ("Harmonic Mean: "), with 'list of numbers', get harmonic mean, and print with a new line.
finally, put text ("Original Array:\n"), and print (list of numbers, with a new line)
exit(0)
.locals
calculate aritmethic mean:
stats(MEAN)
back
calculate the geometric mean:
stats(GEOMEAN)
back
calculatetheharmonicmean:
stats(HARMEAN)
back
</syntaxhighlight>
{{out}}
<pre>
Arithmetic Mean: 5.51
Geometric Mean: 4.47333
Harmonic Mean: 3.29515
Original Array:
4 3 10 6 10 1 1 10 4 1
7 4 5 8 9 7 3 8 1 10
5 5 2 5 8 9 1 5 10 10
6 4 3 5 9 2 6 9 2 9
10 9 3 4 6 2 1 8 10 1
7 5 5 9 9 3 7 9 7 7
9 2 10 1 7 9 3 2 7 4
1 6 2 4 10 7 5 1 5 5
1 2 9 5 10 7 7 6 6 4
3 4 5 2 4 1 10 6 3 7
</pre>
Notice:
<pre>
The line "stats(GEOMEAN)" is identical to:
stats(MULTIPLICATORY),POW BY({1}div by (100))
and...
#defn reciprocalof(_X_) {1},#ATOM#CMPLX,postfix,div,postfix
then:
stats(MULTIPLICATORY),POW BY( reciprocal of (100) )
or...
#defn N-ROOTof(_DATA_,_N_) #ATOM#CMPLX,{1}div by(_N_),postfix,pow,postfix
#define Multiplicatoryof(_DATA_) {_DATA_}stats(MULTIPLICATORY)
then:
N-ROOT of ( Multiplicatory of (list of numbers), 100)
etc.
</pre>
=={{header|APL}}==
<syntaxhighlight lang="apl">
arithmetic←{(+/⍵)÷⍴⍵}
geometric←{(×/⍵)*÷⍴⍵}
harmonic←{(⍴⍵)÷(+/÷⍵)}
x←⍳10
arithmetic x
5.5
geometric x
4.528728688
harmonic x
3.414171521</syntaxhighlight>
=={{header|AppleScript}}==
{{trans|JavaScript}}
<syntaxhighlight lang="applescript">-- 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
script addInverse
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</syntaxhighlight>
{{Out}}
<syntaxhighlight lang="applescript">{values:{arithmetic:5.5, geometric:4.528728688117, harmonic:3.414171521474},
inequalities:{|A >= G|:true}, |G >= H|:true}</syntaxhighlight>
=={{header|Arturo}}==
<syntaxhighlight lang="rebol">arithmeticMean: function [arr]->
average arr
geometricMean: function [arr]->
(product arr) ^ 1//size arr
harmonicMean: function [arr]->
(size arr) // sum map arr 'i [1//i]
print arithmeticMean 1..10
print geometricMean 1..10
print harmonicMean 1..10</syntaxhighlight>
{{out}}
<pre>5.5
4.528728688116765
3.414171521474055</pre>
=={{header|AutoHotkey}}==
<syntaxhighlight lang="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
}</syntaxhighlight>
Message box shows:
<pre>
5.500000
4.528729
3.414172
True
</pre>
=={{header|AWK}}==
<syntaxhighlight lang="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;
}</syntaxhighlight>
=={{header|BBC BASIC}}==
The arithmetic and harmonic means use BBC BASIC's built-in array operations; only the geometric mean needs a loop.
<syntaxhighlight lang="bbcbasic"> 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())
</syntaxhighlight>
{{out}}
<pre>Arithmetic mean = 5.5
Geometric mean = 4.52872869
Harmonic mean = 3.41417152</pre>
=={{header|BQN}}==
<syntaxhighlight lang="bqn">A ← +´÷≠
G ← ≠√×´
H ← A⌾÷
⋈⟜(∧´ ¯1⊸↓ ≥ 1⊸↓) (A∾G∾H) 1+↕10</syntaxhighlight>
{{out}}
<pre>⟨ ⟨ 5.5 4.528728688116765 3.414171521474055 ⟩ 1 ⟩</pre>
=={{header|C}}==
<syntaxhighlight lang="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;
}</syntaxhighlight>
=={{header|C sharp|C#}}==
The standard Linq extension method <tt>Average</tt> provides arithmetic mean. This example adds two more extension methods for the geometric and harmonic means.
{{works with|C sharp|C#|3}}
<syntaxhighlight lang="csharp">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);
}
}
}</syntaxhighlight>
{{out}}
<pre>
Arithmetic mean 5.5
Geometric mean 4.52872868811677
Harmonic mean 3.41417152147406</pre>
=={{header|C++}}==
<syntaxhighlight lang="cpp">#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 ;
}</syntaxhighlight>
{{out}}
<pre>The arithmetic mean is 5.5 , the geometric mean 4.52873 and the harmonic mean 3.41417 !</pre>
=={{header|Clojure}}==
<syntaxhighlight lang="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))</syntaxhighlight>
=={{header|CoffeeScript}}==
<syntaxhighlight lang="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</syntaxhighlight>
{{out}}
<pre>A = 5.5 G = 4.528728688116765 H = 3.414171521474055
A >= G : true G >= H : true</pre>
=={{header|Common Lisp}}==
<syntaxhighlight lang="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)))</syntaxhighlight>
=={{header|Craft Basic}}==
<syntaxhighlight lang="basic">precision 6
define bxsum = 1, sum = 0, sum1i = 0
define average = 0, geometric = 0, harmonic = 0
for i = 1 to 10
let sum = sum + i
let bxsum = bxsum * i
let sum1i = sum1i + (1 / i)
next i
let average = sum / 10
let geometric = bxsum ^ (1 / 10)
let harmonic = 10 / sum1i
print "arithmetic mean: ", average
print "geometric mean: ", geometric
print "harmonic mean: ", harmonic
if average >= geometric and geometric >= harmonic then
print "true"
end
endif
print "false"</syntaxhighlight>
{{out| Output}}<pre>
arithmetic mean: 5.500000
geometric mean: 4.528729
harmonic mean: 3.414172
true
</pre>
=={{header|D}}==
The output for the harmonic mean is wrong.
<syntaxhighlight lang="d">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);
}</syntaxhighlight>
{{out}}
<pre>0.9891573712076470036 4.5287286881167647619 5.5000000000000000000</pre>
=={{header|Delphi}}==
<syntaxhighlight lang="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.</syntaxhighlight>
=={{header|E}}==
Given that we're defining all three together, it makes sense to express their regularities:
<syntaxhighlight lang="e">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 })</syntaxhighlight>
<syntaxhighlight lang="e">? A(1..10)
# value: 5.5
? G(1..10)
# value: 4.528728688116765
? H(1..10)
# value: 3.414171521474055</syntaxhighlight>
=={{header|EasyLang}}==
{{trans|C}}
<syntaxhighlight>
proc mean . v[] a g h .
prod = 1
for v in v[]
sum += v
prod *= v
resum += 1 / v
.
a = sum / len v[]
g = pow prod (1 / len v[])
h = len v[] / resum
.
a[] = [ 1 2 3 4 5 6 7 8 9 10 ]
mean a[] a g h
print a
print g
print h
</syntaxhighlight>
=={{header|EchoLisp}}==
<syntaxhighlight lang="scheme">
(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
</syntaxhighlight>
=={{header|Elixir}}==
<syntaxhighlight lang="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}"</syntaxhighlight>
{{out}}
<pre>
Arithmetic mean: 5.5
Geometric mean: 4.528728688116765
Harmonic mean: 3.414171521474055
(5.5 >= 4.528728688116765 >= 3.414171521474055) is true
</pre>
=={{header|Erlang}}==
<syntaxhighlight lang="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). </syntaxhighlight>
{{out}}
<pre>Arithmetic Mean 5.5
Geometric Mean 4.528728688116765
Harmonic Mean 3.414171521474055 </pre>
=={{header|ERRE}}==
<syntaxhighlight lang="text">
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
</syntaxhighlight>
=={{header|Euler Math Toolbox}}==
<syntaxhighlight lang="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
</syntaxhighlight>
Alternatively, e.g.,
<syntaxhighlight lang="euler math toolbox">
>function G(x) := prod(x)^(1/length(x))
</syntaxhighlight>
=={{header|Euphoria}}==
<syntaxhighlight lang="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)})</syntaxhighlight>
{{out}}
<pre>Arithmetic: 5.5
Geometric: 4.52873
Harmonic: 3.41417
Arithmetic>=Geometric>=Harmonic: true
</pre>
=={{header|Excel}}==
Use the functions : AVERAGE, GEOMEAN and HARMEAN
<syntaxhighlight lang="excel">
=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)
</syntaxhighlight>
{{out}}
<pre>
5.5
4.528728688
3,414171521
</pre>
=={{header|F_Sharp|F#}}==
<syntaxhighlight lang="fsharp">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)</syntaxhighlight>
=={{header|Factor}}==
<syntaxhighlight lang="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 / ;</syntaxhighlight>
( scratchpad ) 10 [1,b] [ a-mean ] [ g-mean ] [ h-mean ] tri
"%f >= %f >= %f\n" printf
5.500000 >= 4.528729 >= 3.414172
=={{header|Fantom}}==
<syntaxhighlight lang="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")
}
}
</syntaxhighlight>
=={{header|Forth}}==
<syntaxhighlight lang="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</syntaxhighlight>
=={{header|Fortran}}==
{{works with|Fortran|90}}
<syntaxhighlight lang="fortran">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</syntaxhighlight>
=={{header|FreeBASIC}}==
<syntaxhighlight lang="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
</syntaxhighlight>
{{out}}
<pre>
Arithmetic mean is : 5.5
Geometric mean is : 4.528728688116765
Harmonic mean is : 3.414171521474055
</pre>
=={{header|FunL}}==
<syntaxhighlight lang="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, (>=)) )</syntaxhighlight>
{{out}}
<pre>
Arithmetic: 11/2 or 5.5
Geometric: 4.528728688116765
Harmonic: 25200/7381 or 3.414171521474055
true
</pre>
=={{header|Futhark}}==
<syntaxhighlight lang="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)
</syntaxhighlight>
=={{header|FutureBasic}}==
<syntaxhighlight lang="FutureBasic>
Double ari = 1, geo = 0, har = 0
Short i, n = 10
for i = 1 to n
ari += i
geo *= i
har += 1 \ i
next
print "ari:", ari \ n
print "geo:", geo^( 1 \ n )
print "har:", n \ har
handleevents
</syntaxhighlight>
<pre>
ari: 5.5
geo: 4.528728688116765
har: 3.414171521474055
</pre>
=={{header|GAP}}==
<syntaxhighlight lang="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</syntaxhighlight>
=={{header|Go}}==
<syntaxhighlight lang="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)
}</syntaxhighlight>
{{out}}
<pre>
A: 5.5 G: 4.528728688116765 H: 3.414171521474055
A >= G >= H: true
</pre>
=={{header|Groovy}}==
Solution:
<syntaxhighlight lang="groovy">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()
}</syntaxhighlight>
Test:
<syntaxhighlight lang="groovy">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}
H: ${H}
"""</syntaxhighlight>
{{out}}
<pre>list: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
A: 5.5
G: 4.528728688116765
H: 3.4141715214</pre>
=={{header|Haskell}}==
====One generalized function====
The [[wp:Generalized mean|general function]] given here yields an arithmetic mean when its first argument is <code>1</code>, a geometric mean when its first argument is <code>0</code>, and a harmonic mean when its first argument is <code>-1</code>.
<
import Control.Monad (zipWithM_)
Line 22 ⟶ 1,544:
mean p xs = (1 / genericLength xs * sum (map (** p) xs)) ** (1/p)
main = do
let ms = zipWith ((. flip mean [1..10]). (,)) "agh" [1, 0, -1]
mapM_ (\(t,m) -> putStrLn $ t : ": " ++ show m) ms
putStrLn $ " a >= g >= h is " ++ show ((\(_,[a,g,h])-> a>=g && g>=h) (unzip ms))</syntaxhighlight>
====Three applicatively defined functions====
These three functions (each combining the length of a list with some kind of fold over the elements of that same list), all share the same applicative structure.
<syntaxhighlight lang="haskell">import Data.List (genericLength)
-- ARITHMETIC, GEOMETRIC AND HARMONIC MEANS ---------------
arithmetic, geometric, harmonic :: [Double] -> Double
arithmetic = (/) . sum <*> genericLength
geometric = (**) . product <*> ((1 /) . genericLength)
harmonic = (/) . genericLength <*> foldr ((+) . (1 /)) 0
-- TEST ---------------------------------------------------
xs :: [Double]
xs = [arithmetic, geometric, harmonic] <*> [[1 .. 10]]
main :: IO ()
main =
(putStrLn . unlines)
[ zip ["Arithmetic", "Geometric", "Harmonic"] xs >>= show
, mappend "\n A >= G >= H is " $ --
(show . and) $ zipWith (>=) xs (tail xs)
]</syntaxhighlight>
{{Out}}
<pre>("Arithmetic",5.5)("Geometric",4.528728688116765)("Harmonic",3.414171521474055)
a >= g >= h is True</pre>
=={{header|HicEst}}==
<syntaxhighlight lang="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)</syntaxhighlight>
! A=5.5; G=4.528728688; H=3.414171521; Result = 1;
=={{header|Icon}} and {{header|Unicon}}==
<syntaxhighlight lang="icon">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
</syntaxhighlight>
{{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:
<syntaxhighlight lang="icon">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</syntaxhighlight>
{{out}}
<pre>#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</pre>
=={{header|IS-BASIC}}==
<syntaxhighlight lang="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</syntaxhighlight>
=={{header|J}}==
'''Solution:'''
<
gmean=: # %: */
hmean=: amean&.:%</
'''Example Usage:'''
<
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:
<syntaxhighlight lang="j">gmean=:amean&.:^.</syntaxhighlight>
(and this variant should probably be preferred - especially if the argument list is long, to avoid problems with floating point infinity.)
=={{header|Java}}==
<syntaxhighlight lang="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));
}
}</syntaxhighlight>
{{out}}
<pre>A = 5.500000 G = 4.528729 H = 3.414172
A >= G is true, G >= H is true</pre>
{{works with|Java|1.8}}
We can rewrite the 3 methods using the new JAVA Stream API:
<syntaxhighlight lang="java">
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 ;
}
}
</syntaxhighlight>
=={{header|JavaScript}}==
===ES5===
<syntaxhighlight lang="javascript">(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);
})();
</syntaxhighlight>
{{Out}}
<syntaxhighlight lang="javascript">{
"values": {
"Arithmetic": 5.5,
"Geometric": 4.528728688116765,
"Harmonic": 3.414171521474055
},
"test": "is A >= G >= H ? yes"
}</syntaxhighlight>
===ES6===
<syntaxhighlight lang="javascript">(() => {
// 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);
})();</syntaxhighlight>
{{Out}}
<syntaxhighlight lang="javascript">{
"values": {
"Arithmetic": 5.5,
"Geometric": 4.528728688116765,
"Harmonic": 3.414171521474055
},
"test": "is A >= G >= H ? yes"
}</syntaxhighlight>
=={{header|jq}}==
<syntaxhighlight lang="jq">def amean: add/length;
def logProduct: map(log) | add;
def gmean: (logProduct / length) | exp;
def hmean: length / (map(1/.) | add);
# Tasks:
[range(1;11) ] | [amean, gmean, hmean] as $ans
| ( $ans[],
"amean > gmean > hmean => \($ans[0] > $ans[1] and $ans[1] > $ans[2] )" )
</syntaxhighlight>
{{Out}}
<pre>5.5
4.528728688116766
3.414171521474055
"amean > gmean > hmean => true"</pre>
=={{header|Julia}}==
Julia has a `mean` function to compute the arithmetic mean of a collections
of numbers. We can redefine it as follows.
<syntaxhighlight lang="julia">amean(A) = sum(A)/length(A)
gmean(A) = prod(A)^(1/length(A))
hmean(A) = length(A)/sum(1./A)</syntaxhighlight>
{{Out}}
<pre>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</pre>
=={{header|K}}==
<syntaxhighlight lang="k">
am:{(+/x)%#x}
gm:{(*/x)^(%#x)}
hm:{(#x)%+/%:'x}
{(am x;gm x;hm x)} 1+!10
5.5 4.528729 3.414172
</syntaxhighlight>
=={{header|Kotlin}}==
<syntaxhighlight lang="kotlin">import kotlin.math.round
import kotlin.math.pow
fun Collection<Double>.geometricMean() =
if (isEmpty()) Double.NaN
else (reduce { n1, n2 -> n1 * n2 }).pow(1.0 / size)
fun Collection<Double>.harmonicMean() =
if (isEmpty() || contains(0.0)) Double.NaN
else size / fold(0.0) { n1, n2 -> n1 + 1.0 / n2 }
fun Double.toFixed(len: Int = 6) =
round(this * 10.0.pow(len)) / 10.0.pow(len)
fun main() {
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 = $a G = ${g.toFixed()} H = ${h.toFixed()}")
println("A >= G is ${a >= g}, G >= H is ${g >= h}")
require(g in h..a)
}</syntaxhighlight>
{{out}}
<pre>A = 5.500000 G = 4.528729 H = 3.414172
A >= G is true, G >= H is true</pre>
=={{header|Lasso}}==
<syntaxhighlight lang="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)</syntaxhighlight>
{{out}}
<pre>5.500000
4.528729
3.414172</pre>
=={{header|Liberty BASIC}}==
<syntaxhighlight lang="lb">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
</syntaxhighlight>
=={{header|Logo}}==
<syntaxhighlight lang="logo">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</syntaxhighlight>
=={{header|Lua}}==
<syntaxhighlight lang="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
--geometric
--harmonic
print(a, g, h)
assert(a >= g and g >= h)</syntaxhighlight>
=={{header|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
<syntaxhighlight lang="m2000 interpreter">
Module CheckIt {
sum=lambda -> {
Read m as array
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
</syntaxhighlight>
=={{header|Maple}}==
<syntaxhighlight lang="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 );
</syntaxhighlight>
{{out}}
<pre>
Arithmeticmean, Geometricmean, Harmonicmean := 5.50000000000000, 4.52872868811677, 3.41417152147406
true
</pre>
=={{header|Mathematica}} / {{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">Print["{Arithmetic Mean, Geometric Mean, Harmonic Mean} = ",
N@Through[{Mean, GeometricMean, HarmonicMean}[Range@10]]]</syntaxhighlight>
{{out}}
<pre>{Arithmetic Mean, Geometric Mean, Harmonic Mean} = {5.5,4.52873,3.41417}</pre>
=={{header|MATLAB}}==
<syntaxhighlight lang="matlab">function [A,G,H] = pythagoreanMeans(list)
A = mean(list);
G = geomean(list);
H = harmmean(list);
end</syntaxhighlight>
A solution that works for both, Matlab and Octave, is this
<syntaxhighlight lang="matlab">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</syntaxhighlight>
Solution:
<syntaxhighlight lang="matlab">>> [A,G,H]=pythagoreanMeans((1:10))
A =
5.500000000000000
G =
4.528728688116765
H =
3.414171521474055</syntaxhighlight>
=={{header|Maxima}}==
<syntaxhighlight lang="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 */</syntaxhighlight>
=={{header|min}}==
<syntaxhighlight lang="min">'avg ^A
(dup product 1 rolldown size / pow) ^G
('size keep (1 swap /) (+) map-reduce /) ^H
(((1 10)) range (((A) (G) (H))) cleave) => (puts!) foreach</syntaxhighlight>
{{out}}
<pre>5.5
4.528728688116765
3.414171521474055</pre>
=={{header|Modula-2}}==
<syntaxhighlight lang="modula2">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.</syntaxhighlight>
=={{header|MUMPS}}==
<syntaxhighlight lang="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</syntaxhighlight>
=={{header|NetRexx}}==
{{trans|ooRexx}}
<syntaxhighlight lang="netrexx">/* 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
</syntaxhighlight>
{{out}}
<pre>
Arithmetic = 5.5, Geometric = 4.528728688116765, Harmonic = 3.4141715214740550062
</pre>
=={{header|Nim}}==
<syntaxhighlight lang="nim">import math, sequtils, sugar
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(1.0 / it))
let numbers = toSeq(1..10).map((x: int) => float(x))
echo amean(numbers), " ", gmean(numbers), " ", hmean(numbers)</syntaxhighlight>
{{out}}
<pre>5.5 4.528728688116765 3.414171521474055</pre>
=={{header|Oberon-2}}==
Oxford Oberon-2
<syntaxhighlight lang="oberon2">
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.
</syntaxhighlight>
{{out}}
<pre>
A(1 .. 10): 5.50000000000
G(1 .. 10): 4.52872868812
H(1 .. 10): 3.41417152147
</pre>
=={{header|Objeck}}==
{{trans|Java}}
<syntaxhighlight lang="objeck">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;
}
}</syntaxhighlight>
Output:
<pre>
A = 5.500, G = 4.529, H = 3.414
A >= G is true, G >= H is true
</pre>
=={{header|OCaml}}==
The three means in one function
<syntaxhighlight lang="ocaml">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)
;;</syntaxhighlight>
{{out}}
<pre>means (Array.init 10 (function i -> (float_of_int (i+1)))) ;;
(* (5.5, 4.5287286881167654, 3.4141715214740551) *)</pre>
Another implementation using <code>[http://caml.inria.fr/pub/docs/manual-ocaml/libref/Array.html#VALfold_left Array.fold_left]</code> instead of a '''for''' loop:
<syntaxhighlight lang="ocaml">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)
;;</syntaxhighlight>
=={{header|Octave}}==
<syntaxhighlight lang="octave">
A = mean(list); % arithmetic mean
G = mean(list,'g'); % geometric mean
H = mean(list,'a'); % harmonic mean
</syntaxhighlight>
See also Matlab implementation [[#MATLAB]]
=={{header|Oforth}}==
<syntaxhighlight lang="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 ]
;</syntaxhighlight>
{{out}}
<pre>
Geometric mean : 4.52872868811677
Arithmetic mean : 5.5 ==> A >= G
Harmonic mean : 3.41417152147406 ==> G >= H
</pre>
=={{header|ooRexx}}==
<syntaxhighlight lang="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</syntaxhighlight>
{{out}}
<pre>Arithmetic = 5.5, Geometric = 4.52872869, Harmonic = 3.41417153</pre>
=={{header|Oz}}==
<syntaxhighlight lang="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</syntaxhighlight>
=={{header|PARI/GP}}==
General implementations:
<syntaxhighlight lang="parigp">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)]</syntaxhighlight>
Specific to the first ''n'' positive integers:
<syntaxhighlight lang="parigp">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]</syntaxhighlight>
These are, asymptotically, n/2, n/e, and n/log n.
=={{header|Pascal}}==
See [[Averages/Pythagorean_means&#Delphi | Delphi]]
=={{header|Perl}}==
<syntaxhighlight lang="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;</syntaxhighlight>
=={{header|Phix}}==
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">arithmetic_mean</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)/</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">geometric_mean</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">product</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">),</span><span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">harmonic_mean</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)/</span><span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_div</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">arithmetic</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">arithmetic_mean</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">geometric</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">geometric_mean</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">harmonic</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">harmonic_mean</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Arithmetic: %.10g\n"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">arithmetic</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Geometric: %.10g\n"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">geometric</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Harmonic: %.10g\n"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">harmonic</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Arithmetic>=Geometric>=Harmonic: %t\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">arithmetic</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">geometric</span> <span style="color: #008080;">and</span> <span style="color: #000000;">geometric</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">harmonic</span><span style="color: #0000FF;">})</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
Arithmetic: 5.5
Geometric: 4.528728688
Harmonic: 3.414171521
Arithmetic>=Geometric>=Harmonic: true
</pre>
=={{header|PHP}}==
<syntaxhighlight lang="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";
</syntaxhighlight>
{{out}}
<pre>
Arithmetic: 5.5
Geometric: 4.5287286881168
Harmonic: 3.4141715214741
</pre>
=={{header|PicoLisp}}==
<syntaxhighlight lang="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 ) ) )</syntaxhighlight>
{{out}}
<pre>Arithmetic mean: 5.500000
Geometric mean: 4.528729
Harmonic mean: 3.414172</pre>
=={{header|PL/I}}==
<syntaxhighlight lang="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);
Line 67 ⟶ 2,854:
put skip data (Geometric);
put skip data (Harmonic);
if Average < Geometric then put skip list ('Error');
if Geometric < Harmonic then put skip list ('Error');
</syntaxhighlight>
Results:
<pre>
AVERAGE= 5.50000E+0000;
GEOMETRIC= 4.52873E+0000;
HARMONIC= 3.41417E+0000;
</pre>
=={{header|PostScript}}==
<syntaxhighlight lang="text">
/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
</syntaxhighlight>
{{out}}
<pre>
Arithmetic Mean : 5.5
Geometric Mean : 4.52873
Harmonic Mean : 3.41417
</pre>
{{libheader|initlib}}
<syntaxhighlight lang="postscript">
/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
</syntaxhighlight>
=={{header|PowerShell}}==
<syntaxhighlight lang="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)"</syntaxhighlight>
{{out}}
<pre>Arithmetic mean: A = 5.5
Geometric mean: G = 4.52872868811676
Harmonic mean: H = 3.41417152147405
Is A >= G ? True
Is G >= H ? True</pre>
=={{header|Processing}}==
<syntaxhighlight lang="processing">void setup() {
float[] numbers = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
println("Arithmetic mean: " + arithmeticMean(numbers));
println("Geometric mean: " + geometricMean(numbers));
println("Harmonic mean: " + harmonicMean(numbers));
}
float arithmeticMean(float[] nums) {
float mean = 0;
for (float n : nums) {
mean += n;
}
mean = mean / nums.length;
return mean;
}
float geometricMean(float[] nums) {
float mean = 1;
for (float n : nums) {
mean *= n;
}
mean = pow(mean, 1.0 / nums.length);
return mean;
}
float harmonicMean(float[] nums) {
float mean = 0;
for (float n : nums) {
mean += 1 / n;
}
mean = nums.length / mean;
return mean;
}</syntaxhighlight>
{{out}}
<pre>Arithmetic mean: 5.5
Geometric mean: 4.528729
Harmonic mean: 3.4141712</pre>
=={{header|PureBasic}}==
<syntaxhighlight lang="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()</syntaxhighlight>
=={{header|Python}}==
{{works with|Python|3}}
<syntaxhighlight lang="python">
from functools import reduce
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</syntaxhighlight>
{{out}}
<pre>5.5 4.52872868812 3.41417152147</pre>
These are the same in Python 2 apart from requiring explicit float division (either through <code>float()</code> casts or float literals such as <code>1./n</code>); or better, do a <code>from __future__ import division</code>, which works on Python 2.2+ as well as Python 3, and makes division work consistently like it does in Python 3.
=={{header|Quackery}}==
Uses <code>root</code> from [[Integer roots#Quackery]].
<syntaxhighlight lang="quackery"> [] 10 times [ i^ 1+ join ]
say "Arithmetic mean:" sp
0 over witheach +
over size 8 point$ echo$
cr
say " Geometric mean:" sp
1 over witheach *
over size 80 ** * 10 root
10 8 ** 8 point$ echo$
cr
say " Harmonic mean:" sp
dup size dip
[ 0 n->v rot
witheach [ n->v 1/v v+ ] ]
n->v 2swap v/ 8 point$ echo$</syntaxhighlight>
{{out}}
<pre>Arithmetic mean: 5.5
Geometric mean: 4.52872868
Harmonic mean: 3.41417152
</pre>
=={{header|R}}==
Initialise x
<syntaxhighlight lang="r">
x <- 1:10
</syntaxhighlight>
Arithmetic mean
<syntaxhighlight lang="r">
a <- sum(x)/length(x)
</syntaxhighlight>
or
<syntaxhighlight lang="r">
a <- mean(x)
</syntaxhighlight>
The geometric mean
<syntaxhighlight lang="r">
g <- prod(x)^(1/length(x))
</syntaxhighlight>
The harmonic mean (no error checking that <math>x_i\ne 0,\text{ } \forall \text{ }i=1\ldots n</math>)
<syntaxhighlight lang="r">
h <- length(x)/sum(1/x)
</syntaxhighlight>
Then:
<syntaxhighlight lang="r">
a > g
</syntaxhighlight>
and
<syntaxhighlight lang="r">
g > h
</syntaxhighlight>
give both
<pre>[1] TRUE</pre>
=={{header|Racket}}==
<syntaxhighlight lang="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))
</syntaxhighlight>
{{out}}
<pre>
5 1/2
4.528728688116765
3 3057/7381
#t
</pre>
=={{header|Raku}}==
(formerly Perl 6)
{{works with|Rakudo|2015.12}}
<syntaxhighlight lang="raku" line>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);
</syntaxhighlight>
{{out}}
<pre>A(1,...,10) = 5.5
G(1,...,10) = 4.52872868811677
H(1,...,10) = 3.41417152147406</pre>
=={{header|REXX}}==
REXX doesn't have a '''POW''' function, so an '''IROOT''' ('''i'''nteger '''root''') function is included here; it includes an
<br>extra error check if used as a general purpose function that would otherwise yield a complex result.
<syntaxhighlight lang="rexx">/*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 " */
if result=="[n/a]" then say '***error***: root' y "can't be even if 1st argument is < 0."
say 'Hmean =' n / rSum /* " " " harmonic " */
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
Iroot: procedure; parse 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 '[n/a]' /*indicate result is "not applicable". */
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*2 /*use this as the first guesstimate. */
d= 5 /*start with 5 dec digs, saves CPU time*/
do until d==a; d= min(d + d, a) /*keep going as digits are increased. */
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 */
g= g * sign(ox); if oy<0 then g= 1 / g /*adjust for original X sign; neg. root*/
numeric digits oDigs; return g / 1 /*normalize to original decimal digits.*/</syntaxhighlight>
{{out|output|text= when using the default input:}}
<pre>
list = 1 2 3 4 5 6 7 8 9 10
Amean = 5.5
Gmean = 4.5287286881167647622
Hmean = 3.4141715214740550062
</pre>
=={{header|Ring}}==
<syntaxhighlight lang="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
</syntaxhighlight>
Output:
<pre>
arithmetic mean = 5.50000000
geometric mean = 4.52872869
harmonic mean = 3.41417152
</pre>
=={{header|RPL}}==
These words can be used either on vectors or lists.
{{works with|HP|28}}
≪ → array op
≪ array 1 GET 2 array SIZE
'''IF''' DUP2 > '''THEN''' DROP2 '''ELSE FOR''' j array GET op EVAL '''NEXT END'''
≫ ≫ '<span style="color:blue">REDUCE</span>' STO
≪ DUP ≪ + ≫ <span style="color:blue">REDUCE</span> SWAP SIZE /
≫ '<span style="color:blue">AMEAN</span>' STO
≪ DUP ≪ * ≫ <span style="color:blue">REDUCE</span> SWAP SIZE INV ^
≫ '<span style="color:blue">GMEAN</span>' STO
≪ SIZE LAST ≪ INV + ≫ <span style="color:blue">REDUCE</span> /
≫ '<span style="color:blue">HMEAN</span>' STO
{ 1 2 3 4 5 6 7 8 9 0 } <span style="color:blue">AMEAN</span>
{ 1 2 3 4 5 6 7 8 9 0 } <span style="color:blue">GMEAN</span>
[ 1 2 3 4 5 6 7 8 9 0 ] <span style="color:blue">HMEAN</span>
{{out}}
<pre>
3: 5.5
2: 4.52872868812
1: 3.41417152147
</pre>
=={{header|Ruby}}==
{{works with|Ruby|1.9+}}
<syntaxhighlight lang="ruby">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)</syntaxhighlight>
{{out}}
<pre>
5.5
4.528728688116765
3.414171521474055
true
</pre>
=={{header|Run BASIC}}==
<syntaxhighlight lang="runbasic">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"</syntaxhighlight>
{{out}}
<pre>
Arithmetic Mean:5.5
Geometric Mean:4.52872869
Harmonic Mean:3.41417132
True</pre>
=={{header|Rust}}==
<syntaxhighlight lang="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");
}
</syntaxhighlight>
{{out}}
<pre>
Average: 5.5, Geometric mean:4.528729, Harmonic mean: 3.4141712
</pre>
=={{header|Scala}}==
{{works with|Scala|2.8+}}
<syntaxhighlight lang="scala">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)</syntaxhighlight>
{{out}}
<pre>Arithmetic mean 5.5
Geometric mean 4.528728688116765
Harmonic mean 3.414171521474055</pre>
=={{header|Scheme}}==
{{Works with|Scheme|R<math>^5</math>RS}}
<syntaxhighlight lang="scheme">(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))</syntaxhighlight>
{{out}}
<syntaxhighlight lang="text">11/2 >= 4.528728688116765 >= 25200/7381
#t</syntaxhighlight>
=={{header|Seed7}}==
<syntaxhighlight lang="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;</syntaxhighlight>
{{out}}
<pre>
Arithmetic mean: 5.5
Geometric mean: 4.528728961944580078125
Harmonic mean: 3.4141712188720703125
</pre>
=={{header|Sidef}}==
<syntaxhighlight lang="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 }</syntaxhighlight>
The same thing, using hyper-operators:
<syntaxhighlight lang="sidef">func A(a) { a«+» / a.len }
func G(a) { a«*» ** (1/a.len) }
func H(a) { a.len / (a«/«1 «+») }</syntaxhighlight>
Calling the functions:
<syntaxhighlight lang="sidef">say("A(1,...,10) = ", A(1..10));
say("G(1,...,10) = ", G(1..10));
say("H(1,...,10) = ", H(1..10));</syntaxhighlight>
{{out}}
<pre>A(1,...,10) = 5.5
G(1,...,10) = 4.528728688116764762203309337195508793499
H(1,...,10) = 3.414171521474055006096734859775098225173</pre>
=={{header|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 /.
<syntaxhighlight lang="smalltalk">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.</syntaxhighlight>
{{out}}
<pre>5.5
4.528728688116765
3.414171521474055
true
true</pre>
=={{header|SQL}}==
It may not be possible to calculate a geometric mean in a query, but the other two are easy enough.
<syntaxhighlight lang="sql">
--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;
</syntaxhighlight>
{{out}}
<pre>
HARM ARITH
---------- ----------
3.41417152 5.5
</pre>
=={{header|Stata}}==
The command [http://www.stata.com/help.cgi?ameans ameans] prints the arithmetic, geometric and harmonic means, together with confidence intervals.
<syntaxhighlight lang="text">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
-----------------------------------------------------------------------------</syntaxhighlight>
=={{header|Swift}}==
<syntaxhighlight lang="text">
// Utility for easy creation of Double from any Numeric
extension Double {
init(withNum v: any Numeric) {
switch v {
case let ii as any BinaryInteger: self.init(ii)
case let ff as any BinaryFloatingPoint: self.init(ff)
default: self.init()
}
}
}
// Extension for numeric collections
extension Collection where Element: Numeric {
var arithmeticMean: Double {
self.reduce(0.0, {$0 + Double(withNum: $1)})/Double(self.count)
}
var geometricMean: Double {
pow(self.reduce(1.0, {$0 * Double(withNum: $1)}), 1.0/Double(self.count))
}
var harmonicMean: Double {
Double(self.count) / self.reduce(0.0, {$0 + 1.0/Double(withNum:$1)})
}
}
//Usage:
var c: [Int] = (1...10).map {$0}
print(c.arithmeticMean)
print(c.geometricMean)
print(c.harmonicMean)
// output:
// 5.5
// 4.528728688116765
// 3.414171521474055
</syntaxhighlight>
=={{header|Tcl}}==
<
set sum 0.0
foreach value $list { set sum [expr {$sum + $value}] }
Line 111 ⟶ 3,595:
puts "A10=$A10, G10=$G10, H10=$H10"
if {$A10 >= $G10} { puts "A10 >= G10" }
if {$G10 >= $H10} { puts "G10 >= H10" }</
{{out}}
<pre>
A10=5.5, G10=4.528728688116765, H10=3.414171521474055
A10 >= G10
G10 >= H10
</pre>
=={{header|Ursala}}==
<syntaxhighlight lang="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></syntaxhighlight>
{{out}}
<pre>(
<5.500000e+00,4.528729e+00,3.414172e+00>,
true)</pre>
=={{header|Vala}}==
Most valac setups will need "-X -lm" added to the compile command to include the C math library.
<syntaxhighlight lang="vala">
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());
}
</syntaxhighlight>
{{out}}
<pre>
Arithmetic mean: 5.5
Geometric mean: 4.5287286881167654
Harmonic mean: 3.4141715214740551
</pre>
=={{header|VBA}}==
Uses Excel VBA.
<syntaxhighlight lang="vb">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</syntaxhighlight>{{out}}
<pre>A = 5,5
G = 4,52872868811677
H = 3,41417152147406 </pre>
=={{header|VBScript}}==
<syntaxhighlight lang="vb">
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))
</syntaxhighlight>
{{Out}}
<pre>
5.5
4.52872868811677
3.41417152147406
</pre>
=={{header|Visual Basic .NET}}==
{{trans|C#}}
<syntaxhighlight lang="vbnet">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</syntaxhighlight>
{{out}}
<pre>Arithmetic mean 5.5
Geometric mean 4.52872868811677
Harmonic mean 3.41417152147406</pre>
=={{header|V (Vlang)}}==
Updated for Vlang version 0.2.2
<syntaxhighlight lang="go">import math
fn main() {
mut sum := 0.0
mut prod :=1.0
mut recip_sum := 0.0
n := 10
for val in 1..(n + 1) {
sum += val
prod *= val
recip_sum = recip_sum + ( 1.0 / val )
}
a := sum / n
g := math.pow( prod, ( 1.0 / f32(n) ) )
h := n / recip_sum
result := 'Arithmetic Mean: ${a:3.2f} \nGeometric Mean: ${g:3.2f}\nHarmonic Mean: ${h:3.2f}'
println( result )
compare := if a >= g && g >= h { "Yes" } else { "Nope" }
println('Is A >= G >= H? $compare')
}</syntaxhighlight>
{{out}}
<pre>Arithmetic Mean: 5.50
Geometric Mean: 4.53
Harmonic Mean: 3.41
Is A >= G >= H? Yes</pre>
=={{header|Wren}}==
<syntaxhighlight lang="wren">var rng = 1..10
var count = rng.count
var A = rng.reduce { |acc, x| acc + x }/count
var G = rng.reduce { |prod, x| prod * x}.pow(1/count)
var H = rng.reduce { |acc, x| acc + 1/x}.pow(-1) * count
System.print("For the numbers %(rng):")
System.print(" Arithmetic mean = %(A)")
System.print(" Geometric mean = %(G)")
System.print(" Harmonic mean = %(H)")
System.print(" A >= G >= H = %(A >= G && G >= H)")</syntaxhighlight>
{{out}}
<pre>
For the numbers 1..10:
Arithmetic mean = 5.5
Geometric mean = 4.5287286881168
Harmonic mean = 3.4141715214741
A >= G >= H = true
</pre>
=={{header|XPL0}}==
<syntaxhighlight lang="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
");
]</syntaxhighlight>
{{out}}
<pre>
5.50000
4.52873
3.41417
ALWAYS DECREASING ORDER
</pre>
=={{header|zkl}}==
<syntaxhighlight lang="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</syntaxhighlight>
{{out}}
<pre>
5.5
4.52873
3.41417
</pre>
| |||