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{{task}}
{{task heading}}
Compute all three of the [[wp:Pythagorean means|Pythagorean means]] of the set of integers 1 through 10 (inclusive).
Show that for this set of positive integers.
-
The most common of the three means, the [[Averages/Arithmetic mean|arithmetic mean]], is the sum of the list divided by its length: :
-
The [[wp:Geometric mean|geometric mean]] is the th root of the product of the list: :
-
The [[wp:Harmonic mean|harmonic mean]] is divided by the sum of the reciprocal of each item in the list: :
{{task heading|See also}}
{{Related tasks/Statistical measures}}
11l
F amean(num)
R sum(num)/Float(num.len)
F gmean(num)
R product(num) ^ (1.0/num.len)
F hmean(num)
return num.len / sum(num.map(n -> 1.0/n))
V numbers = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
print(amean(numbers))
print(gmean(numbers))
print(hmean(numbers))
{{out}}
5.5
4.52873
3.41417
ActionScript
function arithmeticMean(v:Vector.<Number>):Number
{
var sum:Number = 0;
for(var i: uint = 0; i < v.length; i++)
sum += v[i];
return sum/v.length;
}
function geometricMean(v:Vector.<Number>):Number
{
var product:Number = 1;
for(var i: uint = 0; i < v.length; i++)
product *= v[i];
return Math.pow(product, 1/v.length);
}
function harmonicMean(v:Vector.<Number>):Number
{
var sum:Number = 0;
for(var i: uint = 0; i < v.length; i++)
sum += 1/v[i];
return v.length/sum;
}
var list:Vector.<Number> = Vector.<Number>([1,2,3,4,5,6,7,8,9,10]);
trace("Arithmetic: ", arithmeticMean(list));
trace("Geometric: ", geometricMean(list));
trace("Harmonic: ", harmonicMean(list));
Ada
pythagorean_means.ads:
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;
pythagorean_means.adb:
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;
example main.adb:
with Ada.Text_IO;
with Pythagorean_Means;
procedure Main is
My_Set : Pythagorean_Means.Set := (1.0, 2.0, 3.0, 4.0, 5.0,
6.0, 7.0, 8.0, 9.0, 10.0);
Arithmetic_Mean : Float := Pythagorean_Means.Arithmetic_Mean (My_Set);
Geometric_Mean : Float := Pythagorean_Means.Geometric_Mean (My_Set);
Harmonic_Mean : Float := Pythagorean_Means.Harmonic_Mean (My_Set);
begin
Ada.Text_IO.Put_Line (Float'Image (Arithmetic_Mean) & " >= " &
Float'Image (Geometric_Mean) & " >= " &
Float'Image (Harmonic_Mean));
end Main;
ALGOL 68
{{trans|C}} {{wont work with|ALGOL 68|Standard - argc and argv implementation dependent}} {{works with|ALGOL 68G|Any - tested with release [http://sourceforge.net/projects/algol68/files/algol68g/algol68g-1.18.0/algol68g-1.18.0-9h.tiny.el5.centos.fc11.i386.rpm/download 1.18.0-9h.tiny]}} {{wont work with|ELLA ALGOL 68|Any (with appropriate job cards) - argc and argv implementation dependent}}
main: (
INT count:=0;
LONG REAL f, sum:=0, prod:=1, resum:=0;
FORMAT real = $g(0,4)$; # preferred real format #
FILE fbuf; STRING sbuf; associate(fbuf,sbuf);
BOOL opts := TRUE;
FOR i TO argc DO
IF opts THEN # skip args up to the - token #
opts := argv(i) NE "-"
ELSE
rewind(fbuf); sbuf := argv(i); get(fbuf,f);
count +:= 1;
sum +:= f;
prod *:= f;
resum +:= 1/f
FI
OD;
printf(($"c: "f(real)l"s: "f(real)l"p: "f(real)l"r: "f(real)l$,count,sum,prod,resum));
printf(($"Arithmetic mean = "f(real)l$,sum/count));
printf(($"Geometric mean = "f(real)l$,prod**(1/count)));
printf(($"Harmonic mean = "f(real)l$,count/resum))
)
Lunix command: a68g Averages_Pythagorean_means.a68 - 1 2 3 4 5 6 7 8 9 10 {{out}}
c: 10.0000
s: 55.0000
p: 3628800.0000
r: 2.9290
Arithmetic mean = 5.5000
Geometric mean = 4.5287
Harmonic mean = 3.4142
ALGOL W
begin
% returns the arithmetic mean of the elements of n from lo to hi %
real procedure arithmeticMean ( real array n ( * ); integer value lo, hi ) ;
begin
real sum;
sum := 0;
for i := lo until hi do sum := sum + n( i );
sum / ( 1 + ( hi - lo ) )
end arithmeticMean ;
% returns the geometric mean of the elements of n from lo to hi %
real procedure geometricMean ( real array n ( * ); integer value lo, hi ) ;
begin
real product;
product := 1;
for i := lo until hi do product := product * n( i );
exp( ln( product ) / ( 1 + ( hi - lo ) ) )
end geometricMean ;
% returns the harminic mean of the elements of n from lo to hi %
real procedure harmonicMean ( real array n ( * ); integer value lo, hi ) ;
begin
real sum;
sum := 0;
for i := lo until hi do sum := sum + ( 1 / n( i ) );
( 1 + ( hi - lo ) ) / sum
end harmonicMean ;
real array v ( 1 :: 10 );
for i := 1 until 10 do v( i ) := i;
r_w := 10; r_d := 5; r_format := "A"; s_w := 0; % set output format %
write( "Arithmetic mean: ", arithmeticMean( v, 1, 10 ) );
write( "Geometric mean: ", geometricMean( v, 1, 10 ) );
write( "Harmonic mean: ", harmonicMean( v, 1, 10 ) )
end.
{{out}}
Arithmetic mean: 5.50000
Geometric mean: 4.52872
Harmonic mean: 3.41417
APL
arithmetic←{(+/⍵)÷⍴⍵}
geometric←{(×/⍵)*÷⍴⍵}
harmonic←{(⍴⍵)÷(+/÷⍵)}
x←⍳10
arithmetic x
5.5
geometric x
4.528728688
harmonic x
3.414171521
AppleScript
{{trans|JavaScript}}
-- arithmetic_mean :: [Number] -> Number
on arithmetic_mean(xs)
-- sum :: Number -> Number -> Number
script sum
on |λ|(accumulator, x)
accumulator + x
end |λ|
end script
foldl(sum, 0, xs) / (length of xs)
end arithmetic_mean
-- geometric_mean :: [Number] -> Number
on geometric_mean(xs)
-- product :: Number -> Number -> Number
script product
on |λ|(accumulator, x)
accumulator * x
end |λ|
end script
foldl(product, 1, xs) ^ (1 / (length of xs))
end geometric_mean
-- harmonic_mean :: [Number] -> Number
on harmonic_mean(xs)
-- addInverse :: Number -> Number -> Number
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
{{Out}}
{values:{arithmetic:5.5, geometric:4.528728688117, harmonic:3.414171521474},
inequalities:{|A >= G|:true}, |G >= H|:true}
AutoHotkey
A := ArithmeticMean(1, 10)
G := GeometricMean(1, 10)
H := HarmonicMean(1, 10)
If G Between %H% And %A%
Result := "True"
Else
Result := "False"
MsgBox, %A%`n%G%`n%H%`n%Result%
;---------------------------------------------------------------------------
ArithmeticMean(a, b) { ; of integers a through b
;---------------------------------------------------------------------------
n := b - a + 1
Loop, %n%
Sum += (a + A_Index - 1)
Return, Sum / n
}
;---------------------------------------------------------------------------
GeometricMean(a, b) { ; of integers a through b
;---------------------------------------------------------------------------
n := b - a + 1
Prod := 1
Loop, %n%
Prod *= (a + A_Index - 1)
Return, Prod ** (1 / n)
}
;---------------------------------------------------------------------------
HarmonicMean(a, b) { ; of integers a through b
;---------------------------------------------------------------------------
n := b - a + 1
Loop, %n%
Sum += 1 / (a + A_Index - 1)
Return, n / Sum
}
Message box shows:
5.500000
4.528729
3.414172
True
AWK
#!/usr/bin/awk -f
{
x = $1; # value of 1st column
A += x;
G += log(x);
H += 1/x;
N++;
}
END {
print "Arithmethic mean: ",A/N;
print "Geometric mean : ",exp(G/N);
print "Harmonic mean : ",N/H;
}
BBC BASIC
The arithmetic and harmonic means use BBC BASIC's built-in array operations; only the geometric mean needs a loop.
DIM a(9)
a() = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
PRINT "Arithmetic mean = " ; FNarithmeticmean(a())
PRINT "Geometric mean = " ; FNgeometricmean(a())
PRINT "Harmonic mean = " ; FNharmonicmean(a())
END
DEF FNarithmeticmean(a())
= SUM(a()) / (DIM(a(),1)+1)
DEF FNgeometricmean(a())
LOCAL a, I%
a = 1
FOR I% = 0 TO DIM(a(),1)
a *= a(I%)
NEXT
= a ^ (1/(DIM(a(),1)+1))
DEF FNharmonicmean(a())
LOCAL b()
DIM b(DIM(a(),1))
b() = 1/a()
= (DIM(a(),1)+1) / SUM(b())
{{out}}
Arithmetic mean = 5.5
Geometric mean = 4.52872869
Harmonic mean = 3.41417152
C
#include <stdio.h>
#include <stdlib.h> // atoi()
#include <math.h> // pow()
int main(int argc, char* argv[])
{
int i, count=0;
double f, sum=0.0, prod=1.0, resum=0.0;
for (i=1; i<argc; ++i) {
f = atof(argv[i]);
count++;
sum += f;
prod *= f;
resum += (1.0/f);
}
//printf(" c:%d\n s:%f\n p:%f\n r:%f\n",count,sum,prod,resum);
printf("Arithmetic mean = %f\n",sum/count);
printf("Geometric mean = %f\n",pow(prod,(1.0/count)));
printf("Harmonic mean = %f\n",count/resum);
return 0;
}
C++
#include <vector>
#include <iostream>
#include <numeric>
#include <cmath>
#include <algorithm>
double toInverse ( int i ) {
return 1.0 / i ;
}
int main( ) {
std::vector<int> numbers ;
for ( int i = 1 ; i < 11 ; i++ )
numbers.push_back( i ) ;
double arithmetic_mean = std::accumulate( numbers.begin( ) , numbers.end( ) , 0 ) / 10.0 ;
double geometric_mean =
pow( std::accumulate( numbers.begin( ) , numbers.end( ) , 1 , std::multiplies<int>( ) ), 0.1 ) ;
std::vector<double> inverses ;
inverses.resize( numbers.size( ) ) ;
std::transform( numbers.begin( ) , numbers.end( ) , inverses.begin( ) , toInverse ) ;
double harmonic_mean = 10 / std::accumulate( inverses.begin( ) , inverses.end( ) , 0.0 ); //initial value of accumulate must be a double!
std::cout << "The arithmetic mean is " << arithmetic_mean << " , the geometric mean "
<< geometric_mean << " and the harmonic mean " << harmonic_mean << " !\n" ;
return 0 ;
}
{{out}}
The arithmetic mean is 5.5 , the geometric mean 4.52873 and the harmonic mean 3.41417 !
C#
The standard Linq extension method Average provides arithmetic mean. This example adds two more extension methods for the geometric and harmonic means.
{{works with|C sharp|C#|3}}
using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
namespace PythMean
{
static class Program
{
static void Main(string[] args) {
var nums = from n in Enumerable.Range(1, 10) select (double)n;
var a = nums.Average();
var g = nums.Gmean();
var h = nums.Hmean();
Console.WriteLine("Arithmetic mean {0}", a);
Console.WriteLine("Geometric mean {0}", g);
Console.WriteLine("Harmonic mean {0}", h);
Debug.Assert(a >= g && g >= h);
}
// Geometric mean extension method.
static double Gmean(this IEnumerable<double> n) {
return Math.Pow(n.Aggregate((s, i) => s * i), 1.0 / n.Count());
}
// Harmonic mean extension method.
static double Hmean(this IEnumerable<double> n) {
return n.Count() / n.Sum(i => 1.0 / i);
}
}
}
{{out}}
Arithmetic mean 5.5
Geometric mean 4.52872868811677
Harmonic mean 3.41417152147406
CoffeeScript
a = [ 1..10 ]
arithmetic_mean = (a) -> a.reduce(((s, x) -> s + x), 0) / a.length
geometic_mean = (a) -> Math.pow(a.reduce(((s, x) -> s * x), 1), (1 / a.length))
harmonic_mean = (a) -> a.length / a.reduce(((s, x) -> s + 1 / x), 0)
A = arithmetic_mean a
G = geometic_mean a
H = harmonic_mean a
console.log "A = ", A, " G = ", G, " H = ", H
console.log "A >= G : ", A >= G, " G >= H : ", G >= H
{{out}}
A = 5.5 G = 4.528728688116765 H = 3.414171521474055
A >= G : true G >= H : true
Common Lisp
(defun generic-mean (nums reduce-op final-op)
(funcall final-op (reduce reduce-op nums)))
(defun a-mean (nums)
(generic-mean nums #'+ (lambda (x) (/ x (length nums)))))
(defun g-mean (nums)
(generic-mean nums #'* (lambda (x) (expt x (/ 1 (length nums))))))
(defun h-mean (nums)
(generic-mean nums
(lambda (x y) (+ x
(/ 1 y)))
(lambda (x) (/ (length nums) x))))
(let ((numbers (loop for i from 1 to 10 collect i)))
(let ((a-mean (a-mean numbers))
(g-mean (g-mean numbers))
(h-mean (h-mean numbers)))
(assert (> a-mean g-mean h-mean))
(format t "a-mean ~a~%" a-mean)
(format t "g-mean ~a~%" g-mean)
(format t "h-mean ~a~%" h-mean)))
Clojure
(use '[clojure.contrib.math :only (expt)])
(defn a-mean [coll]
(/ (apply + coll) (count coll)))
(defn g-mean [coll]
(expt (apply * coll) (/ (count coll))))
(defn h-mean [coll]
(/ (count coll) (apply + (map / coll))))
(let [numbers (range 1 11)
a (a-mean numbers) g (g-mean numbers) h (h-mean numbers)]
(println a ">=" g ">=" h)
(>= a g h))
D
The output for the harmonic mean is wrong.
import std.stdio, std.algorithm, std.range, std.functional;
auto aMean(T)(T data) pure nothrow @nogc {
return data.sum / data.length;
}
auto gMean(T)(T data) pure /*@nogc*/ {
return data.reduce!q{a * b} ^^ (1.0 / data.length);
}
auto hMean(T)(T data) pure /*@nogc*/ {
return data.length / data.reduce!q{ 1.0 / a + b };
}
void main() {
immutable m = [adjoin!(hMean, gMean, aMean)(iota(1.0L, 11.0L))[]];
writefln("%(%.19f %)", m);
assert(m.isSorted);
}
{{out}}
0.9891573712076470036 4.5287286881167647619 5.5000000000000000000
Delphi
program AveragesPythagoreanMeans;
{$APPTYPE CONSOLE}
uses Types, Math;
function ArithmeticMean(aArray: TDoubleDynArray): Double;
var
lValue: Double;
begin
Result := 0;
for lValue in aArray do
Result := Result + lValue;
if Result > 0 then
Result := Result / Length(aArray);
end;
function GeometricMean(aArray: TDoubleDynArray): Double;
var
lValue: Double;
begin
Result := 1;
for lValue in aArray do
Result := Result * lValue;
Result := Power(Result, 1 / Length(aArray));
end;
function HarmonicMean(aArray: TDoubleDynArray): Double;
var
lValue: Double;
begin
Result := 0;
for lValue in aArray do
Result := Result + 1 / lValue;
Result := Length(aArray) / Result;
end;
var
lSourceArray: TDoubleDynArray;
AMean, GMean, HMean: Double;
begin
lSourceArray := TDoubleDynArray.Create(1,2,3,4,5,6,7,8,9,10);
AMean := ArithmeticMean(lSourceArray));
GMean := GeometricMean(lSourceArray));
HMean := HarmonicMean(lSourceArray));
if (AMean >= GMean) and (GMean >= HMean) then
Writeln(AMean, " ≥ ", GMean, " ≥ ", HMean)
else
writeln("Error!");
end.
E
Given that we're defining all three together, it makes sense to express their regularities:
def makeMean(base, include, finish) {
return def mean(numbers) {
var count := 0
var acc := base
for x in numbers {
acc := include(acc, x)
count += 1
}
return finish(acc, count)
}
}
def A := makeMean(0, fn b,x { b+x }, fn acc,n { acc / n })
def G := makeMean(1, fn b,x { b*x }, fn acc,n { acc ** (1/n) })
def H := makeMean(0, fn b,x { b+1/x }, fn acc,n { n / acc })
? A(1..10)
# value: 5.5
? G(1..10)
# value: 4.528728688116765
? H(1..10)
# value: 3.414171521474055
EchoLisp
(define (A xs) (// (for/sum ((x xs)) x) (length xs)))
(define (G xs) (expt (for/product ((x xs)) x) (// (length xs))))
(define (H xs) (// (length xs) (for/sum ((x xs)) (// x))))
(define xs (range 1 11))
(and (>= (A xs) (G xs)) (>= (G xs) (H xs)))
→ #t
Elixir
defmodule Means do
def arithmetic(list) do
Enum.sum(list) / length(list)
end
def geometric(list) do
:math.pow(Enum.reduce(list, &(*/2)), 1 / length(list))
end
def harmonic(list) do
1 / arithmetic(Enum.map(list, &(1 / &1)))
end
end
list = Enum.to_list(1..10)
IO.puts "Arithmetic mean: #{am = Means.arithmetic(list)}"
IO.puts "Geometric mean: #{gm = Means.geometric(list)}"
IO.puts "Harmonic mean: #{hm = Means.harmonic(list)}"
IO.puts "(#{am} >= #{gm} >= #{hm}) is #{am >= gm and gm >= hm}"
{{out}}
Arithmetic mean: 5.5
Geometric mean: 4.528728688116765
Harmonic mean: 3.414171521474055
(5.5 >= 4.528728688116765 >= 3.414171521474055) is true
Erlang
%% Author: Abhay Jain <abhay_1303@yahoo.co.in>
-module(mean_calculator).
-export([find_mean/0]).
find_mean() ->
%% This is function calling. First argument is the the beginning number
%% and second argument is the initial value of sum for AM & HM and initial value of product for GM.
arithmetic_mean(1, 0),
geometric_mean(1, 1),
harmonic_mean(1, 0).
%% Function to calculate Arithmetic Mean
arithmetic_mean(Number, Sum) when Number > 10 ->
AM = Sum / 10,
io:format("Arithmetic Mean ~p~n", [AM]);
arithmetic_mean(Number, Sum) ->
NewSum = Sum + Number,
arithmetic_mean(Number+1, NewSum).
%% Function to calculate Geometric Mean
geometric_mean(Number, Product) when Number > 10 ->
GM = math:pow(Product, 0.1),
io:format("Geometric Mean ~p~n", [GM]);
geometric_mean(Number, Product) ->
NewProd = Product * Number,
geometric_mean(Number+1, NewProd).
%% Function to calculate Harmonic Mean
harmonic_mean(Number, Sum) when Number > 10 ->
HM = 10 / Sum,
io:format("Harmonic Mean ~p~n", [HM]);
harmonic_mean(Number, Sum) ->
NewSum = Sum + (1/Number),
harmonic_mean(Number+1, NewSum).
{{out}}
Arithmetic Mean 5.5
Geometric Mean 4.528728688116765
Harmonic Mean 3.414171521474055
ERRE
DIM A[9]
PROCEDURE ARITHMETIC_MEAN(A[]->M) LOCAL S,I% NEL%=UBOUND(A,1) S=0 FOR I%=0 TO NEL% DO S+=A[I%] END FOR M=S/(NEL%+1) END PROCEDURE
PROCEDURE GEOMETRIC_MEAN(A[]->M) LOCAL S,I% NEL%=UBOUND(A,1) S=1 FOR I%=0 TO NEL% DO S*=A[I%] END FOR M=S^(1/(NEL%+1)) END PROCEDURE
PROCEDURE HARMONIC_MEAN(A[]->M) LOCAL S,I% NEL%=UBOUND(A,1) S=0 FOR I%=0 TO NEL% DO S+=1/A[I%] END FOR M=(NEL%+1)/S END PROCEDURE
BEGIN A[]=(1,2,3,4,5,6,7,8,9,10) ARITHMETIC_MEAN(A[]->M) PRINT("Arithmetic mean = ";M) GEOMETRIC_MEAN(A[]->M) PRINT("Geometric mean = ";M) HARMONIC_MEAN(A[]->M) PRINT("Harmonic mean = ";M) END PROGRAM
## Euler Math Toolbox
```Euler Math Toolbox
>function A(x) := mean(x)
>function G(x) := exp(mean(log(x)))
>function H(x) := 1/mean(1/x)
>x=1:10; A(x), G(x), H(x)
5.5
4.52872868812
3.41417152147
Alternatively, e.g.,
>function G(x) := prod(x)^(1/length(x))
Euphoria
function arithmetic_mean(sequence s)
atom sum
if length(s) = 0 then
return 0
else
sum = 0
for i = 1 to length(s) do
sum += s[i]
end for
return sum/length(s)
end if
end function
function geometric_mean(sequence s)
atom p
p = 1
for i = 1 to length(s) do
p *= s[i]
end for
return power(p,1/length(s))
end function
function harmonic_mean(sequence s)
atom sum
if length(s) = 0 then
return 0
else
sum = 0
for i = 1 to length(s) do
sum += 1/s[i]
end for
return length(s) / sum
end if
end function
function true_or_false(atom x)
if x then
return "true"
else
return "false"
end if
end function
constant s = {1,2,3,4,5,6,7,8,9,10}
constant arithmetic = arithmetic_mean(s),
geometric = geometric_mean(s),
harmonic = harmonic_mean(s)
printf(1,"Arithmetic: %g\n", arithmetic)
printf(1,"Geometric: %g\n", geometric)
printf(1,"Harmonic: %g\n", harmonic)
printf(1,"Arithmetic>=Geometric>=Harmonic: %s\n",
{true_or_false(arithmetic>=geometric and geometric>=harmonic)})
{{out}}
Arithmetic: 5.5
Geometric: 4.52873
Harmonic: 3.41417
Arithmetic>=Geometric>=Harmonic: true
Excel
Use the functions : AVERAGE, GEOMEAN and HARMEAN
=AVERAGE(1;2;3;4;5;6;7;8;9;10)
=GEOMEAN(1;2;3;4;5;6;7;8;9;10)
=HARMEAN(1;2;3;4;5;6;7;8;9;10)
{{out}}
5.5
4.528728688
3,414171521
=={{header|F_Sharp|F#}}==
let P = [1.0; 2.0; 3.0; 4.0; 5.0; 6.0; 7.0; 8.0; 9.0; 10.0]
let arithmeticMean (x : float list) =
x |> List.sum
|> (fun acc -> acc / float (List.length(x)))
let geometricMean (x: float list) =
x |> List.reduce (*)
|> (fun acc -> Math.Pow(acc, 1.0 / (float (List.length(x)))))
let harmonicMean (x: float list) =
x |> List.map (fun a -> 1.0 / a)
|> List.sum
|> (fun acc -> float (List.length(x)) / acc)
printfn "Arithmetic Mean: %A" (arithmeticMean P)
printfn "Geometric Mean: %A" (geometricMean P)
printfn "Harmonic Mean: %A" (harmonicMean P)
Factor
: a-mean ( seq -- mean )
[ sum ] [ length ] bi / ;
: g-mean ( seq -- mean )
[ product ] [ length recip ] bi ^ ;
: h-mean ( seq -- mean )
[ length ] [ [ recip ] map-sum ] bi / ;
( scratchpad ) 10 [1,b] [ a-mean ] [ g-mean ] [ h-mean ] tri "%f >= %f >= %f\n" printf 5.500000 >= 4.528729 >= 3.414172
Fantom
class Main
{
static Float arithmeticMean (Int[] nums)
{
if (nums.size == 0) return 0.0f
sum := 0
nums.each |n| { sum += n }
return sum.toFloat / nums.size
}
static Float geometricMean (Int[] nums)
{
if (nums.size == 0) return 0.0f
product := 1
nums.each |n| { product *= n }
return product.toFloat.pow(1f/nums.size)
}
static Float harmonicMean (Int[] nums)
{
if (nums.size == 0) return 0.0f
reciprocals := 0f
nums.each |n| { reciprocals += 1f / n }
return nums.size.toFloat / reciprocals
}
public static Void main ()
{
items := (1..10).toList
// display results
echo (arithmeticMean (items))
echo (geometricMean (items))
echo (harmonicMean (items))
// check given relation
if ((arithmeticMean (items) >= geometricMean (items)) &&
(geometricMean (items) >= harmonicMean (items)))
echo ("relation holds")
else
echo ("relation failed")
}
}
Forth
: famean ( faddr n -- f )
0e
tuck floats bounds do
i f@ f+
float +loop
0 d>f f/ ;
: fgmean ( faddr n -- f )
1e
tuck floats bounds do
i f@ f*
float +loop
0 d>f 1/f f** ;
: fhmean ( faddr n -- f )
dup 0 d>f 0e
floats bounds do
i f@ 1/f f+
float +loop
f/ ;
create test 1e f, 2e f, 3e f, 4e f, 5e f, 6e f, 7e f, 8e f, 9e f, 10e f,
test 10 famean fdup f.
test 10 fgmean fdup fdup f.
test 10 fhmean fdup f.
( A G G H )
f>= . f>= . \ -1 -1
Fortran
{{works with|Fortran|90}}
program Mean
real :: a(10) = (/ (i, i=1,10) /)
real :: amean, gmean, hmean
amean = sum(a) / size(a)
gmean = product(a)**(1.0/size(a))
hmean = size(a) / sum(1.0/a)
if ((amean < gmean) .or. (gmean < hmean)) then
print*, "Error!"
else
print*, amean, gmean, hmean
end if
end program Mean
FreeBASIC
' FB 1.05.0 Win64
Function ArithmeticMean(array() As Double) As Double
Dim length As Integer = Ubound(array) - Lbound(array) + 1
Dim As Double sum = 0.0
For i As Integer = LBound(array) To UBound(array)
sum += array(i)
Next
Return sum/length
End Function
Function GeometricMean(array() As Double) As Double
Dim length As Integer = Ubound(array) - Lbound(array) + 1
Dim As Double product = 1.0
For i As Integer = LBound(array) To UBound(array)
product *= array(i)
Next
Return product ^ (1.0 / length)
End Function
Function HarmonicMean(array() As Double) As Double
Dim length As Integer = Ubound(array) - Lbound(array) + 1
Dim As Double sum = 0.0
For i As Integer = LBound(array) To UBound(array)
sum += 1.0 / array(i)
Next
Return length / sum
End Function
Dim vector(1 To 10) As Double
For i As Integer = 1 To 10
vector(i) = i
Next
Print "Arithmetic mean is :"; ArithmeticMean(vector())
Print "Geometric mean is :"; GeometricMean(vector())
Print "Harmonic mean is :"; HarmonicMean(vector())
Print
Print "Press any key to quit the program"
Sleep
{{out}}
Arithmetic mean is : 5.5
Geometric mean is : 4.528728688116765
Harmonic mean is : 3.414171521474055
FunL
import lists.zip
def
mean( s, 0 ) = product( s )^(1/s.length())
mean( s, p ) = (1/s.length() sum( x^p | x <- s ))^(1/p)
def
monotone( [_], _ ) = true
monotone( a1:a2:as, p ) = p( a1, a2 ) and monotone( a2:as, p )
means = [mean( 1..10, m ) | m <- [1, 0, -1]]
for (m, l) <- zip( means, ['Arithmetic', 'Geometric', 'Harmonic'] )
println( "$l: $m" + (if m is Rational then " or ${m.doubleValue()}" else '') )
println( monotone(means, (>=)) )
{{out}}
Arithmetic: 11/2 or 5.5
Geometric: 4.528728688116765
Harmonic: 25200/7381 or 3.414171521474055
true
Futhark
fun arithmetic_mean(as: [n]f64): f64 =
reduce (+) 0.0 (map (/f64(n)) as)
fun geometric_mean(as: [n]f64): f64 =
reduce (*) 1.0 (map (**(1.0/f64(n))) as)
fun harmonic_mean(as: [n]f64): f64 =
f64(n) / reduce (+) 0.0 (map (1.0/) as)
fun main(as: [n]f64): (f64,f64,f64) =
(arithmetic_mean as,
geometric_mean as,
harmonic_mean as)
GAP
# The first two work with rationals or with floats
# (but bear in mind that support of floating point is very poor in GAP)
mean := v -> Sum(v) / Length(v);
harmean := v -> Length(v) / Sum(v, Inverse);
geomean := v -> EXP_FLOAT(Sum(v, LOG_FLOAT) / Length(v));
mean([1 .. 10]);
# 11/2
harmean([1 .. 10]);
# 25200/7381
v := List([1..10], FLOAT_INT);;
mean(v);
# 5.5
harmean(v);
# 3.41417
geomean(v);
# 4.52873
Go
package main
import (
"fmt"
"math"
)
func main() {
sum, sumr, prod := 0., 0., 1.
for n := 1.; n <= 10; n++ {
sum += n
sumr += 1 / n
prod *= n
}
a, g, h := sum/10, math.Pow(prod, .1), 10/sumr
fmt.Println("A:", a, "G:", g, "H:", h)
fmt.Println("A >= G >= H:", a >= g && g >= h)
}
{{out}}
A: 5.5 G: 4.528728688116765 H: 3.414171521474055
A >= G >= H: true
Groovy
Solution:
def arithMean = { list ->
list == null \
? null \
: list.empty \
? 0 \
: list.sum() / list.size()
}
def geomMean = { list ->
list == null \
? null \
: list.empty \
? 1 \
: list.inject(1) { prod, item -> prod*item } ** (1 / list.size())
}
def harmMean = { list ->
list == null \
? null \
: list.empty \
? 0 \
: list.size() / list.collect { 1.0/it }.sum()
}
Test:
def list = 1..10
def A = arithMean(list)
def G = geomMean(list)
assert A >= G
def H = harmMean(list)
assert G >= H
println """
list: ${list}
A: ${A}
G: ${G}
H: ${H}
"""
{{out}}
list: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
A: 5.5
G: 4.528728688116765
H: 3.4141715214
Haskell
=One generalized function=
The [[wp:Generalized mean|general function]] given here yields an arithmetic mean when its first argument is 1, a geometric mean when its first argument is 0, and a harmonic mean when its first argument is -1.
import Data.List (genericLength)
import Control.Monad (zipWithM_)
mean :: Double -> [Double] -> Double
mean 0 xs = product xs ** (1 / genericLength xs)
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))
=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.
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)
]
{{Out}}
("Arithmetic",5.5)("Geometric",4.528728688116765)("Harmonic",3.414171521474055)
a >= g >= h is True
HicEst
AGH = ALIAS( A, G, H ) ! named vector elements
AGH = (0, 1, 0)
DO i = 1, 10
A = A + i
G = G * i
H = H + 1/i
ENDDO
AGH = (A/10, G^0.1, 10/H)
WRITE(ClipBoard, Name) AGH, "Result = " // (A>=G) * (G>=H)
! A=5.5; G=4.528728688; H=3.414171521; Result = 1;
=={{header|Icon}} and {{header|Unicon}}==
link numbers # for a/g/h means
procedure main()
every put(x := [], 1 to 10)
writes("x := [ "); every writes(!x," "); write("]")
write("Arithmetic mean:", a := amean!x)
write("Geometric mean:",g := gmean!x)
write("Harmonic mean:", h := hmean!x)
write(" a >= g >= h is ", if a >= g >= h then "true" else "false")
end
{{libheader|Icon Programming Library}} [http://www.cs.arizona.edu/icon/library/src/procs/numbers.icn numbers:amean, numbers:gmean, and numbers:hmean] are shown below:
procedure amean(L[]) #: arithmetic mean
local m
if *L = 0 then fail
m := 0.0
every m +:= !L
return m / *L
end
procedure gmean(L[]) #: geometric mean
local m
if *L = 0 then fail
m := 1.0
every m *:= !L
m := abs(m)
if m > 0.0 then
return exp (log(m) / *L)
else
fail
end
procedure hmean(L[]) #: harmonic mean
local m, r
if *L = 0 then fail
m := 0.0
every r := !L do {
if r = 0.0 then fail
else m +:= 1.0 / r
}
return *L / m
end
{{out}}
#means.exe
x := [ 1 2 3 4 5 6 7 8 9 10 ]
Arithmetic mean:5.5
Geometric mean:4.528728688116765
Harmonic mean:3.414171521474055
a >= g >= h is true
=={{header|IS-BASIC}}==
## J
'''Solution:'''
```j
amean=: +/ % #
gmean=: # %: */
hmean=: amean&.:%
'''Example Usage:'''
(amean , gmean , hmean) >: i. 10
5.5 4.528729 3.414172
assert 2 >:/\ (amean , gmean , hmean) >: i. 10 NB. check amean >= gmean and gmean >= hmean
Note that gmean could have instead been defined as mean under logarithm, for example:
gmean=:amean&.:^.
(and this variant should probably be preferred - especially if the argument list is long, to avoid problems with floating point infinity.)
Java
import java.util.Arrays;
import java.util.List;
public class PythagoreanMeans {
public static double arithmeticMean(List<Double> numbers) {
if (numbers.isEmpty()) return Double.NaN;
double mean = 0.0;
for (Double number : numbers) {
mean += number;
}
return mean / numbers.size();
}
public static double geometricMean(List<Double> numbers) {
if (numbers.isEmpty()) return Double.NaN;
double mean = 1.0;
for (Double number : numbers) {
mean *= number;
}
return Math.pow(mean, 1.0 / numbers.size());
}
public static double harmonicMean(List<Double> numbers) {
if (numbers.isEmpty() || numbers.contains(0.0)) return Double.NaN;
double mean = 0.0;
for (Double number : numbers) {
mean += (1.0 / number);
}
return numbers.size() / mean;
}
public static void main(String[] args) {
Double[] array = {1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0};
List<Double> list = Arrays.asList(array);
double arithmetic = arithmeticMean(list);
double geometric = geometricMean(list);
double harmonic = harmonicMean(list);
System.out.format("A = %f G = %f H = %f%n", arithmetic, geometric, harmonic);
System.out.format("A >= G is %b, G >= H is %b%n", (arithmetic >= geometric), (geometric >= harmonic));
}
}
{{out}}
A = 5.500000 G = 4.528729 H = 3.414172
A >= G is true, G >= H is true
{{works with|Java|1.8}} We can rewrite the 3 methods using the new JAVA Stream API:
public static double arithmAverage(double array[]){
if (array == null ||array.length == 0) {
return 0.0;
}
else {
return DoubleStream.of(array).average().getAsDouble();
}
}
public static double geomAverage(double array[]){
if (array == null ||array.length == 0) {
return 0.0;
}
else {
double aver = DoubleStream.of(array).reduce(1, (x, y) -> x * y);
return Math.pow(aver, 1.0 / array.length);
}
}
public static double harmAverage(double array[]){
if (array == null ||array.length == 0) {
return 0.0;
}
else {
double aver = DoubleStream.of(array)
// remove null values
.filter(n -> n > 0.0)
// generate 1/n array
.map( n-> 1.0/n)
// accumulating
.reduce(0, (x, y) -> x + y);
// just this reduce is not working- need to do in 2 steps
// .reduce(0, (x, y) -> 1.0/x + 1.0/y);
return array.length / aver ;
}
}
JavaScript
ES5
(function () {
'use strict';
// arithmetic_mean :: [Number] -> Number
function arithmetic_mean(ns) {
return (
ns.reduce( // sum
function (sum, n) {
return (sum + n);
},
0
) / ns.length
);
}
// geometric_mean :: [Number] -> Number
function geometric_mean(ns) {
return Math.pow(
ns.reduce( // product
function (product, n) {
return (product * n);
},
1
),
1 / ns.length
);
}
// harmonic_mean :: [Number] -> Number
function harmonic_mean(ns) {
return (
ns.length / ns.reduce( // sum of inverses
function (invSum, n) {
return (invSum + (1 / n));
},
0
)
);
}
var values = [arithmetic_mean, geometric_mean, harmonic_mean]
.map(function (f) {
return f([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]);
}),
mean = {
Arithmetic: values[0], // arithmetic
Geometric: values[1], // geometric
Harmonic: values[2] // harmonic
}
return JSON.stringify({
values: mean,
test: "is A >= G >= H ? " +
(
mean.Arithmetic >= mean.Geometric &&
mean.Geometric >= mean.Harmonic ? "yes" : "no"
)
}, null, 2);
})();
{{Out}}
{
"values": {
"Arithmetic": 5.5,
"Geometric": 4.528728688116765,
"Harmonic": 3.414171521474055
},
"test": "is A >= G >= H ? yes"
}
ES6
(() => {
// arithmeticMean :: [Number] -> Number
const arithmeticMean = xs =>
foldl((sum, n) => sum + n, 0, xs) / length(xs);
// geometricMean :: [Number] -> Number
const geometricMean = xs =>
raise(foldl((product, x) => product * x, 1, xs), 1 / length(xs));
// harmonicMean :: [Number] -> Number
const harmonicMean = xs =>
length(xs) / foldl((invSum, n) => invSum + (1 / n), 0, xs);
// GENERIC FUNCTIONS ------------------------------------------------------
// A list of functions applied to a list of arguments
// <*> :: [(a -> b)] -> [a] -> [b]
const ap = (fs, xs) => //
[].concat.apply([], fs.map(f => //
[].concat.apply([], xs.map(x => [f(x)]))));
// foldl :: (b -> a -> b) -> b -> [a] -> b
const foldl = (f, a, xs) => xs.reduce(f, a);
// length :: [a] -> Int
const length = xs => xs.length;
// mapFromList :: [(k, v)] -> Dictionary
const mapFromList = kvs =>
foldl((a, [k, v]) =>
(a[(typeof k === 'string' && k) || show(k)] = v, a), {}, kvs);
// raise :: Num -> Int -> Num
const raise = (n, e) => Math.pow(n, e);
// show :: a -> String
// show :: a -> Int -> String
const show = (...x) =>
JSON.stringify.apply(
null, x.length > 1 ? [x[0], null, x[1]] : x
);
// zip :: [a] -> [b] -> [(a,b)]
const zip = (xs, ys) =>
xs.slice(0, Math.min(xs.length, ys.length))
.map((x, i) => [x, ys[i]]);
// TEST -------------------------------------------------------------------
// mean :: Dictionary
const mean = mapFromList(zip(
['Arithmetic', 'Geometric', 'Harmonic'],
ap([arithmeticMean, geometricMean, harmonicMean], [
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
])
));
return show({
values: mean,
test: `is A >= G >= H ? ${mean.Arithmetic >= mean.Geometric &&
mean.Geometric >= mean.Harmonic ? "yes" : "no"}`
}, 2);
})();
{{Out}}
{
"values": {
"Arithmetic": 5.5,
"Geometric": 4.528728688116765,
"Harmonic": 3.414171521474055
},
"test": "is A >= G >= H ? yes"
}
jq
def amean: add/length;
def 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] )" )
{{Out}}
5.5
4.528728688116766
3.414171521474055
"amean > gmean > hmean => true"
Julia
Julia has a mean function to compute the arithmetic mean of a collections
of numbers. We can redefine it as follows.
amean(A) = sum(A)/length(A)
gmean(A) = prod(A)^(1/length(A))
hmean(A) = length(A)/sum(1./A)
{{Out}}
julia> map(f-> f(1:10), [amean, gmean, hmean])
3-element Array{Float64,1}:
5.5
4.52873
3.41417
julia> ans[1] > ans[2] > ans[3]
true
K
am:{(+/x)%#x}
gm:{(*/x)^(%#x)}
hm:{(#x)%+/%:'x}
{(am x;gm x;hm x)} 1+!10
5.5 4.528729 3.414172
Kotlin
.geometricMean() =
if (isEmpty()) Double.NaN
else Math.pow(reduce { n1, n2 -> n1 * n2 }, 1.0 / size)
fun Collection<Double>.harmonicMean() =
if (isEmpty() || contains(0.0)) Double.NaN
else size / reduce { n1, n2 -> n1 + 1.0 / n2 }
fun main(args: Array<String>) {
val list = listOf(1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0)
val a = list.average() // arithmetic mean
val g = list.geometricMean()
val h = list.harmonicMean()
println("A = %f G = %f H = %f".format(a, g, h))
println("A >= G is %b, G >= H is %b".format(a >= g, g >= h))
require(g in h..a)
}
{{out}}
A = 5.500000 G = 4.528729 H = 3.414172
A >= G is true, G >= H is true
Lasso
define arithmetic_mean(a::staticarray)::decimal => {
//sum of the list divided by its length
return (with e in #a sum #e) / decimal(#a->size)
}
define geometric_mean(a::staticarray)::decimal => {
// The geometric mean is the nth root of the product of the list
local(prod = 1)
with e in #a do => { #prod *= #e }
return math_pow(#prod,1/decimal(#a->size))
}
define harmonic_mean(a::staticarray)::decimal => {
// The harmonic mean is n divided by the sum of the reciprocal of each item in the list
return decimal(#a->size)/(with e in #a sum 1/decimal(#e))
}
arithmetic_mean(generateSeries(1,10)->asStaticArray)
geometric_mean(generateSeries(1,10)->asStaticArray)
harmonic_mean(generateSeries(1,10)->asStaticArray)
{{out}}
5.500000
4.528729
3.414172
Liberty BASIC
for i = 1 to 10
a = a + i
next
ArithmeticMean = a/10
b = 1
for i = 1 to 10
b = b * i
next
GeometricMean = b ^ (1/10)
for i = 1 to 10
c = c + (1/i)
next
HarmonicMean = 10/c
print "ArithmeticMean: ";ArithmeticMean
print "Geometric Mean: ";GeometricMean
print "Harmonic Mean: ";HarmonicMean
if (ArithmeticMean>=GeometricMean) and (GeometricMean>=HarmonicMean) then
print "True"
else
print "False"
end if
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
Lua
function fsum(f, a, ...) return a and f(a) + fsum(f, ...) or 0 end
function pymean(t, f, finv) return finv(fsum(f, unpack(t)) / #t) end
nums = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
--arithmetic
a = pymean(nums, function(n) return n end, function(n) return n end)
--geometric
g = pymean(nums, math.log, math.exp)
--harmonic
h = pymean(nums, function(n) return 1/n end, function(n) return 1/n end)
print(a, g, h)
assert(a >= g and g >= h)
M2000 Interpreter
Dimension(m,0) is the base (lower bound) for each dimension in an array, and can be 0 or 1. Len(a) or len(M()) return length of a pointer to array and an array, as number of array elements. For one dimension arrays len() is equal to Dimension(m(),1) where 1 is the first dimension Dim A(10,10) : Print Len(A())=100
Module CheckIt {
sum=lambda -> {
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
Maple
x := [ seq( 1 .. 10 ) ];
Means := proc( x )
uses Statistics;
return Mean( x ), GeometricMean( x ), HarmonicMean( x );
end proc:
Arithmeticmean, Geometricmean, Harmonicmean := Means( x );
is( Arithmeticmean >= Geometricmean and Geometricmean >= Harmonicmean );
{{out}}
Arithmeticmean, Geometricmean, Harmonicmean := 5.50000000000000, 4.52872868811677, 3.41417152147406
true
=={{header|Mathematica}} / {{header|Wolfram Language}}==
Print["{Arithmetic Mean, Geometric Mean, Harmonic Mean} = ",
N@Through[{Mean, GeometricMean, HarmonicMean}[Range@10]]]
{{out}}
{Arithmetic Mean, Geometric Mean, Harmonic Mean} = {5.5,4.52873,3.41417}
MATLAB
function [A,G,H] = pythagoreanMeans(list)
A = mean(list);
G = geomean(list);
H = harmmean(list);
end
A solution that works for both, Matlab and Octave, is this
function [A,G,H] = pythagoreanMeans(list)
A = mean(list); % arithmetic mean
G = exp(mean(log(list))); % geometric mean
H = 1./mean(1./list); % harmonic mean
end
Solution:
[A,G,H]=pythagoreanMeans((1:10))
A =
5.500000000000000
G =
4.528728688116765
H =
3.414171521474055
Maxima
/* built-in */
L: makelist(i, i, 1, 10)$
mean(L), numer; /* 5.5 */
geometric_mean(L), numer; /* 4.528728688116765 */
harmonic_mean(L), numer; /* 3.414171521474055 */
=={{header|Modula-2}}==
MODULE PythagoreanMeans;
FROM FormatString IMPORT FormatString;
FROM LongMath IMPORT power;
FROM LongStr IMPORT RealToStr;
FROM Terminal IMPORT WriteString,WriteLn,ReadChar;
PROCEDURE ArithmeticMean(numbers : ARRAY OF LONGREAL) : LONGREAL;
VAR
i,cnt : CARDINAL;
mean : LONGREAL;
BEGIN
mean := 0.0;
cnt := 0;
FOR i:=0 TO HIGH(numbers) DO
mean := mean + numbers[i];
INC(cnt);
END;
RETURN mean / LFLOAT(cnt)
END ArithmeticMean;
PROCEDURE GeometricMean(numbers : ARRAY OF LONGREAL) : LONGREAL;
VAR
i,cnt : CARDINAL;
mean : LONGREAL;
BEGIN
mean := 1.0;
cnt := 0;
FOR i:=0 TO HIGH(numbers) DO
mean := mean * numbers[i];
INC(cnt);
END;
RETURN power(mean, 1.0 / LFLOAT(cnt))
END GeometricMean;
PROCEDURE HarmonicMean(numbers : ARRAY OF LONGREAL) : LONGREAL;
VAR
i,cnt : CARDINAL;
mean : LONGREAL;
BEGIN
mean := 0.0;
cnt := 0;
FOR i:=0 TO HIGH(numbers) DO
mean := mean + ( 1.0 / numbers[i]);
INC(cnt);
END;
RETURN LFLOAT(cnt) / mean
END HarmonicMean;
CONST Size = 10;
TYPE DA = ARRAY[1..Size] OF LONGREAL;
VAR
buf : ARRAY[0..63] OF CHAR;
array : DA;
arithmetic,geometric,harmonic : LONGREAL;
BEGIN
array := DA{1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0};
arithmetic := ArithmeticMean(array);
geometric := GeometricMean(array);
harmonic := HarmonicMean(array);
WriteString("A = ");
RealToStr(arithmetic, buf);
WriteString(buf);
WriteString(" G = ");
RealToStr(geometric, buf);
WriteString(buf);
WriteString(" H = ");
RealToStr(harmonic, buf);
WriteString(buf);
WriteLn;
FormatString("A >= G is %b, G >= H is %b\n", buf, arithmetic >= geometric, geometric >= harmonic);
WriteString(buf);
ReadChar
END PythagoreanMeans.
MUMPS
Pyth(n) New a,ii,g,h,x
For ii=1:1:n set x(ii)=ii
;
; Average
Set a=0 For ii=1:1:n Set a=a+x(ii)
Set a=a/n
;
; Geometric
Set g=1 For ii=1:1:n Set g=g*x(ii)
Set g=g**(1/n)
;
; Harmonic
Set h=0 For ii=1:1:n Set h=1/x(ii)+h
Set h=n/h
;
Write !,"Pythagorean means for 1..",n,":",!
Write "Average = ",a," >= Geometric ",g," >= harmonic ",h,!
Quit
Do Pyth(10)
Pythagorean means for 1..10:
Average = 5.5 >= Geometric 4.528728688116178495 >= harmonic 3.414171521474055006
NetRexx
{{trans|ooRexx}}
/* NetRexx */
options replace format comments java crossref symbols nobinary
numeric digits 20
a1 = ArrayList(Arrays.asList([Rexx 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0]))
say "Arithmetic =" arithmeticMean(a1)", Geometric =" geometricMean(a1)", Harmonic =" harmonicMean(a1)
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method arithmeticMean(numbers = java.util.List) public static returns Rexx
-- somewhat arbitrary return for ooRexx
if numbers.isEmpty then return "NaN"
mean = 0
number = Rexx
loop number over numbers
mean = mean + number
end
return mean / numbers.size
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method geometricMean(numbers = java.util.List) public static returns Rexx
-- somewhat arbitrary return for ooRexx
if numbers.isEmpty then return "NaN"
mean = 1
number = Rexx
loop number over numbers
mean = mean * number
end
return Math.pow(mean, 1 / numbers.size)
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method harmonicMean(numbers = java.util.List) public static returns Rexx
-- somewhat arbitrary return for ooRexx
if numbers.isEmpty then return "NaN"
mean = 0
number = Rexx
loop number over numbers
if number = 0 then return "Nan"
mean = mean + (1 / number)
end
-- problem here...
return numbers.size / mean
{{out}}
Arithmetic = 5.5, Geometric = 4.528728688116765, Harmonic = 3.4141715214740550062
Nim
import math, sequtils, future
proc amean(num: seq[float]): float =
sum(num) / float(len(num))
proc gmean(num: seq[float]): float =
result = 1
for n in num: result *= n
result = pow(result, 1.0 / float(num.len))
proc hmean(num: seq[float]): float =
for n in num: result += 1.0 / n
result = float(num.len) / result
proc ameanFunctional(num: seq[float]): float =
sum(num) / float(num.len)
proc gmeanFunctional(num: seq[float]): float =
num.foldl(a * b).pow(1.0 / float(num.len))
proc hmeanFunctional(num: seq[float]): float =
float(num.len) / sum(num.mapIt(float, 1.0 / it))
let numbers = toSeq(1..10).map((x: int) => float(x))
echo amean(numbers), " ", gmean(numbers), " ", hmean(numbers)
{{out}}
5.5000000000000000e+00 4.5287286881167654e+00 3.4141715214740551e+00
=={{header|Oberon-2}}== Oxford Oberon-2
MODULE PythMean;
IMPORT Out, ML := MathL;
PROCEDURE Triplets(a: ARRAY OF INTEGER;VAR triplet: ARRAY OF LONGREAL);
VAR
i: INTEGER;
BEGIN
triplet[0] := 0.0;triplet[1] := 0.0; triplet[2] := 0.0;
FOR i:= 0 TO LEN(a) - 1 DO
triplet[0] := triplet[0] + a[i];
triplet[1] := triplet[1] + ML.Ln(a[i]);
triplet[2] := triplet[2] + (1 / a[i])
END
END Triplets;
PROCEDURE Means*(a: ARRAY OF INTEGER);
VAR
triplet: ARRAY 3 OF LONGREAL;
BEGIN
Triplets(a,triplet);
Out.String("A(1 .. 10): ");Out.LongReal(triplet[0] / LEN(a));Out.Ln;
Out.String("G(1 .. 10): ");Out.LongReal(ML.Exp(triplet[1]/ LEN(a)));Out.Ln;
Out.String("H(1 .. 10): ");Out.LongReal(LEN(a) / triplet[2]);Out.Ln;
END Means;
VAR
nums: ARRAY 10 OF INTEGER;
i: INTEGER;
BEGIN
FOR i := 0 TO LEN(nums) - 1 DO
nums[i] := i + 1
END;
Means(nums)
END PythMean.
{{out}}
A(1 .. 10): 5.50000000000
G(1 .. 10): 4.52872868812
H(1 .. 10): 3.41417152147
Objeck
{{trans|Java}}
class PythagMeans {
function : Main(args : String[]) ~ Nil {
array := [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0];
arithmetic := ArithmeticMean(array);
geometric := GeometricMean(array);
harmonic := HarmonicMean(array);
arith_geo := arithmetic >= geometric;
geo_harm := geometric >= harmonic;
"A = {$arithmetic}, G = {$geometric}, H = {$harmonic}"->PrintLine();
"A >= G is {$arith_geo}, G >= H is {$geo_harm}"->PrintLine();
}
function : native : ArithmeticMean(numbers : Float[]) ~ Float {
if(numbers->Size() = 0) { return -1.0; };
mean := 0.0;
each(i : numbers) {
mean += numbers[i];
};
return mean / numbers->Size();
}
function : native : GeometricMean(numbers : Float[]) ~ Float {
if(numbers->Size() = 0) { return -1.0; };
mean := 1.0;
each(i : numbers) {
mean *= numbers[i];
};
return mean->Power(1.0 / numbers->Size());
}
function : native : HarmonicMean(numbers : Float[]) ~ Float {
if(numbers->Size() = 0) { return -1.0; };
mean := 0.0;
each(i : numbers) {
mean += (1.0 / numbers[i]);
};
return numbers->Size() / mean;
}
}
Output:
A = 5.500, G = 4.529, H = 3.414
A >= G is true, G >= H is true
OCaml
The three means in one function
let means v =
let n = Array.length v
and a = ref 0.0
and b = ref 1.0
and c = ref 0.0 in
for i=0 to n-1 do
a := !a +. v.(i);
b := !b *. v.(i);
c := !c +. 1.0/.v.(i);
done;
let nn = float_of_int n in
(!a /. nn, !b ** (1.0/.nn), nn /. !c)
;;
{{out}}
means (Array.init 10 (function i -> (float_of_int (i+1)))) ;;
(* (5.5, 4.5287286881167654, 3.4141715214740551) *)
Another implementation using [http://caml.inria.fr/pub/docs/manual-ocaml/libref/Array.html#VALfold_left Array.fold_left] instead of a '''for''' loop:
let means v =
let (a, b, c) =
Array.fold_left
(fun (a, b, c) x -> (a+.x, b*.x, c+.1./.x))
(0.,1.,0.) v
in
let n = float_of_int (Array.length v) in
(a /. n, b ** (1./.n), n /. c)
;;
Octave
A = mean(list); % arithmetic mean
G = mean(list,'g'); % geometric mean
H = mean(list,'a'); % harmonic mean
See also Matlab implementation [[#MATLAB]]
Oforth
import: mapping
: A ( x )
x sum
x size dup ifZero: [ 2drop null ] else: [ >float / ]
;
: G( x ) #* x reduce x size inv powf ;
: H( x ) x size x map( #inv ) sum / ;
: averages
| g |
"Geometric mean :" . 10 seq G dup .cr ->g
"Arithmetic mean :" . 10 seq A dup . g >= ifTrue: [ " ==> A >= G" .cr ]
"Harmonic mean :" . 10 seq H dup . g <= ifTrue: [ " ==> G >= H" .cr ]
;
{{out}}
Geometric mean : 4.52872868811677
Arithmetic mean : 5.5 ==> A >= G
Harmonic mean : 3.41417152147406 ==> G >= H
ooRexx
a = .array~of(1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0)
say "Arithmetic =" arithmeticMean(a)", Geometric =" geometricMean(a)", Harmonic =" harmonicMean(a)
::routine arithmeticMean
use arg numbers
-- somewhat arbitrary return for ooRexx
if numbers~isEmpty then return "NaN"
mean = 0
loop number over numbers
mean += number
end
return mean / numbers~items
::routine geometricMean
use arg numbers
-- somewhat arbitrary return for ooRexx
if numbers~isEmpty then return "NaN"
mean = 1
loop number over numbers
mean *= number
end
return rxcalcPower(mean, 1 / numbers~items)
::routine harmonicMean
use arg numbers
-- somewhat arbitrary return for ooRexx
if numbers~isEmpty then return "NaN"
mean = 0
loop number over numbers
if number = 0 then return "Nan"
mean += 1 / number
end
-- problem here....
return numbers~items / mean
::requires rxmath LIBRARY
{{out}}
Arithmetic = 5.5, Geometric = 4.52872869, Harmonic = 3.41417153
Oz
declare
%% helpers
fun {Sum Xs} {FoldL Xs Number.'+' 0.0} end
fun {Product Xs} {FoldL Xs Number.'*' 1.0} end
fun {Len Xs} {Int.toFloat {Length Xs}} end
fun {AMean Xs}
{Sum Xs}
/
{Len Xs}
end
fun {GMean Xs}
{Pow
{Product Xs}
1.0/{Len Xs}}
end
fun {HMean Xs}
{Len Xs}
/
{Sum {Map Xs fun {$ X} 1.0 / X end}}
end
Numbers = {Map {List.number 1 10 1} Int.toFloat}
[A G H] = [{AMean Numbers} {GMean Numbers} {HMean Numbers}]
in
{Show [A G H]}
A >= G = true
G >= H = true
PARI/GP
General implementations:
arithmetic(v)={
sum(i=1,#v,v[i])/#v
};
geometric(v)={
prod(i=1,#v,v[i])^(1/#v)
};
harmonic(v)={
#v/sum(i=1,#v,1/v[i])
};
v=vector(10,i,i);
[arithmetic(v),geometric(v),harmonic(v)]
Specific to the first ''n'' positive integers:
arithmetic_first(n)={
(n+1)/2
};
geometric_first(n)={
n!^(1/n)
};
harmonic_first(n)={
n/if(n>1000,
log(n)+Euler+1/(n+n)+1/(12*n^2)-1/(120*n^4)+1/(252*n^6)-1/(240*n^8)+1/(132*n^10)
,
n/sum(k=1,n,1/k)
)
};
[arithmetic_first(10),geometric_first(10),harmonic_first(10)]
%[1]>=%[2] && %[2] >= %[3]
These are, asymptotically, n/2, n/e, and n/log n.
Pascal
See [[Averages/Pythagorean_means&#Delphi | Delphi]]
Perl
sub A
{
my $a = 0;
$a += $_ for @_;
return $a / @_;
}
sub G
{
my $p = 1;
$p *= $_ for @_;
return $p**(1/@_); # power of 1/n == root of n
}
sub H
{
my $h = 0;
$h += 1/$_ for @_;
return @_/$h;
}
my @ints = (1..10);
my $a = A(@ints);
my $g = G(@ints);
my $h = H(@ints);
print "A=$a\nG=$g\nH=$h\n";
die "Error" unless $a >= $g and $g >= $h;
Perl 6
{{works with|Rakudo|2015.12}}
sub A { ([+] @_) / @_ }
sub G { ([*] @_) ** (1 / @_) }
sub H { @_ / [+] 1 X/ @_ }
say "A(1,...,10) = ", A(1..10);
say "G(1,...,10) = ", G(1..10);
say "H(1,...,10) = ", H(1..10);
{{out}}
A(1,...,10) = 5.5
G(1,...,10) = 4.52872868811677
H(1,...,10) = 3.41417152147406
Phix
(note to self: iff should really be a builtin)
function arithmetic_mean(sequence s)
return sum(s)/length(s)
end function
function geometric_mean(sequence s)
atom p = 1
for i=1 to length(s) do
p *= s[i]
end for
return power(p,1/length(s))
end function
function harmonic_mean(sequence s)
atom rsum = 0
for i=1 to length(s) do
rsum += 1/s[i]
end for
return length(s)/rsum
end function
function iff(integer condition, object Tval, object Fval)
if condition then return Tval else return Fval end if
end function
constant s = {1,2,3,4,5,6,7,8,9,10}
constant arithmetic = arithmetic_mean(s),
geometric = geometric_mean(s),
harmonic = harmonic_mean(s)
printf(1,"Arithmetic: %.10g\n", arithmetic)
printf(1,"Geometric: %.10g\n", geometric)
printf(1,"Harmonic: %.10g\n", harmonic)
printf(1,"Arithmetic>=Geometric>=Harmonic: %s\n", {iff((arithmetic>=geometric and geometric>=harmonic),"true","false")})
{{out}}
Arithmetic: 5.5
Geometric: 4.528728688
Harmonic: 3.414171521
Arithmetic>=Geometric>=Harmonic: true
PHP
<?php
// Created with PHP 7.0
function ArithmeticMean(array $values)
{
return array_sum($values) / count($values);
}
function GeometricMean(array $values)
{
return array_product($values) ** (1 / count($values));
}
function HarmonicMean(array $values)
{
$sum = 0;
foreach ($values as $value) {
$sum += 1 / $value;
}
return count($values) / $sum;
}
$values = array(1, 2, 3, 4, 5, 6, 7, 8, 9, 10);
echo "Arithmetic: " . ArithmeticMean($values) . "\n";
echo "Geometric: " . GeometricMean($values) . "\n";
echo "Harmonic: " . HarmonicMean($values) . "\n";
{{out}}
Arithmetic: 5.5
Geometric: 4.5287286881168
Harmonic: 3.4141715214741
PicoLisp
(load "@lib/math.l")
(let (Lst (1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0) Len (length Lst))
(prinl "Arithmetic mean: "
(format
(/ (apply + Lst) Len)
*Scl ) )
(prinl "Geometric mean: "
(format
(pow (*/ (apply * Lst) (** 1.0 (dec Len))) (/ 1.0 Len))
*Scl ) )
(prinl "Harmonic mean: "
(format
(*/ (* 1.0 Len) 1.0 (sum '((N) (*/ 1.0 1.0 N)) Lst))
*Scl ) ) )
{{out}}
Arithmetic mean: 5.500000
Geometric mean: 4.528729
Harmonic mean: 3.414172
PL/I
declare n fixed binary,
(Average, Geometric, Harmonic) float;
declare A(10) float static initial (1,2,3,4,5,6,7,8,9,10);
n = hbound(A,1);
/* compute the average */
Average = sum(A)/n;
/* Compute the geometric mean: */
Geometric = prod(A)**(1/n);
/* Compute the Harmonic mean: */
Harmonic = n / sum(1/A);
put skip data (Average);
put skip data (Geometric);
put skip data (Harmonic);
if Average < Geometric then put skip list ('Error');
if Geometric < Harmonic then put skip list ('Error');
Results:
AVERAGE= 5.50000E+0000;
GEOMETRIC= 4.52873E+0000;
HARMONIC= 3.41417E+0000;
PostScript
x{ /sum sum i add def /prod prod i mul def /invsum invsum i -1 exp add def /i i 1 add def }repeat (Arithmetic Mean : ) print sum x div = (Geometric Mean : ) print prod x -1 exp exp = (Harmonic Mean : ) print x invsum div = }def
10 pythamean
{{out}}
```txt
Arithmetic Mean : 5.5
Geometric Mean : 4.52873
Harmonic Mean : 3.41417
{{libheader|initlib}}
/numbers {[1 10] 1 range}.
/recip {1 exch div}.
% Arithmetic mean
numbers dup 0 {+} fold exch length div
% Geometric mean
numbers dup 1 {*} fold exch length recip exp
% Harmonic mean
numbers dup 0 {recip +} fold exch length exch div
PowerShell
$A = 0
$LogG = 0
$InvH = 0
$ii = 1..10
foreach($i in $ii) {
# Arithmetic mean is computed directly
$A += $i / $ii.Count
# Geometric mean is computed using Logarithms
$LogG += [Math]::Log($i) / $ii.Count
# Harmonic mean is computed using its inverse
$InvH += 1 / ($i * $ii.Count)
}
$G = [Math]::Exp($LogG)
$H = 1/$InvH
write-host "Arithmetic mean: A = $A"
write-host "Geometric mean: G = $G"
write-host "Harmonic mean: H = $H"
write-host "Is A >= G ? $($A -ge $G)"
write-host "Is G >= H ? $($G -ge $H)"
{{out}}
Arithmetic mean: A = 5.5
Geometric mean: G = 4.52872868811676
Harmonic mean: H = 3.41417152147405
Is A >= G ? True
Is G >= H ? True
PureBasic
Procedure.d ArithmeticMean()
For a = 1 To 10
mean + a
Next
ProcedureReturn mean / 10
EndProcedure
Procedure.d GeometricMean()
mean = 1
For a = 1 To 10
mean * a
Next
ProcedureReturn Pow(mean, 1 / 10)
EndProcedure
Procedure.d HarmonicMean()
For a = 1 To 10
mean.d + 1 / a
Next
ProcedureReturn 10 / mean
EndProcedure
If HarmonicMean() <= GeometricMean() And GeometricMean() <= ArithmeticMean()
Debug "true"
EndIf
Debug ArithmeticMean()
Debug GeometricMean()
Debug HarmonicMean()
Python
{{works with|Python|3}}
from operator import mul
from functools import reduce
def amean(num):
return sum(num) / len(num)
def gmean(num):
return reduce(mul, num, 1)**(1 / len(num))
def hmean(num):
return len(num) / sum(1 / n for n in num)
numbers = range(1, 11) # 1..10
a, g, h = amean(numbers), gmean(numbers), hmean(numbers)
print(a, g, h)
assert a >= g >= h
{{out}}
5.5 4.52872868812 3.41417152147
These are the same in Python 2 apart from requiring explicit float division (either through float() casts or float literals such as 1./n); or better, do a from future import division, which works on Python 2.2+ as well as Python 3, and makes division work consistently like it does in Python 3.
R
Initialise x
x <- 1:10
Arithmetic mean
a <- sum(x)/length(x)
or
a <- mean(x)
The geometric mean
g <- prod(x)^(1/length(x))
The harmonic mean (no error checking that )
h <- length(x)/sum(1/x)
Then:
a > g
and
g > h
give both
[1] TRUE
Racket
#lang racket
(define (arithmetic xs)
(/ (for/sum ([x xs]) x)
(length xs)))
(define (geometric xs)
(expt (for/product ([x xs]) x)
(/ (length xs))))
(define (harmonic xs)
(/ (length xs)
(for/sum ([x xs]) (/ x))))
(define xs (range 1 11))
(arithmetic xs)
(geometric xs)
(harmonic xs)
(>= (arithmetic xs) (geometric xs) (harmonic xs))
{{out}}
5 1/2
4.528728688116765
3 3057/7381
#t
REXX
REXX doesn't have a '''POW''' function, so an '''IROOT''' ('''i'''nteger '''root''') function is included here; it includes an
extra error check if used as a general purpose function that would otherwise yield a complex result.
/*REXX program computes and displays the Pythagorean means [Amean, Gmean, Hmean]. */
numeric digits 20 /*use a little extra for the precision.*/
parse arg n . /*obtain the optional argument from CL.*/
if n=='' | n=="," then n=10 /*None specified? Then use the default*/
sum=0; prod=1; rSum=0 /*initialize sum/product/reciprocal sum*/
$=; do #=1 for n; $=$ # /*generate list by appending # to list.*/
sum = sum + # /*compute the sum of all the elements. */
prod= prod * # /*compute the product of all elements. */
rSum= rSum + 1/# /*compute the sum of the reciprocals. */
end /*#*/
say ' list ='$ /*display the list of numbers used. */
say 'Amean =' sum / n /*calculate & display arithmetic mean.*/
say 'Gmean =' Iroot(prod, n) /* " " " geometric " */
say 'Hmean =' n / rSum /* " " " harmonic " */
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
Iroot: procedure; arg x 1 ox, y 1 oy /*get both args, and also a copy of X&Y*/
if x=0 | x=1 | y=1 then return x /*handle special case of zero and unity*/
if y=0 then return 1 /* " " " " a zero root.*/
if x<0 & y//2==0 then return IrootErr()
x=abs(x); y=abs(y); m=y - 1 /*use the absolute value for X and Y. */
oDigs=digits(); a=oDigs + 5 /*save original digits; add five digs.*/
g=(x+1) / y**y /*use this as the first guesstimate. */
d=5 /*start with 5 dec digs, saves CPU time*/
do until d==a /*keep going as digits are increased. */
d=min(d+d, a); numeric digits d; f=d-2 /*limit digits to original digits + 5.*/
og= /*use a non-guess for the old G (guess)*/
do forever; gm=g**m /*keep computing at the Yth root. */
_=format( (m*g*gm + x) / (y*gm), , f) /*this is the nitty─gritty calculation.*/
if _=g | _=og then leave /*are we close enough yet? */
og=g; g=_ /*save guess ──► OG; set the new guess.*/
end /*forever*/
end /*until */
if oy<0 then g=1/g /*use reciprocal when Y is negative. */
numeric digits oDigs; return sign(ox)*g/1 /*normalize to original decimal digits.*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
IrootErr: say '***error*** (from Iroot): root' y "can't be even if 1st argument is < 0."
return '[n/a]' /*return a "not applicable" string. */
'''output''' using the default inputs:
list = 1 2 3 4 5 6 7 8 9 10
Amean = 5.5
Gmean = 4.5287286881167647622
Hmean = 3.4141715214740550062
Ring
decimals(8)
array = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
see "arithmetic mean = " + arithmeticMean(array) + nl
see "geometric mean = " + geometricMean(array) + nl
see "harmonic mean = " + harmonicMean(array) + nl
func arithmeticMean a
return summary(a) / len(a)
func geometricMean a
b = 1
for i = 1 to len(a)
b *= a[i]
next
return pow(b, (1/len(a)))
func harmonicMean a
b = list(len(a))
for nr = 1 to len(a)
b[nr] = 1/a[nr]
next
return len(a) / summary(b)
func summary s
sum = 0
for n = 1 to len(s)
sum += s[n]
next
return sum
Output:
arithmetic mean = 5.50000000
geometric mean = 4.52872869
harmonic mean = 3.41417152
Ruby
{{works with|Ruby|1.9+}}
class Array
def arithmetic_mean
inject(0.0, :+) / length
end
def geometric_mean
inject(:*) ** (1.0 / length)
end
def harmonic_mean
length / inject(0.0) {|s, m| s + 1.0/m}
end
end
class Range
def method_missing(m, *args)
case m
when /_mean$/ then to_a.send(m)
else super
end
end
end
p a = (1..10).arithmetic_mean
p g = (1..10).geometric_mean
p h = (1..10).harmonic_mean
# is h < g < a ??
p g.between?(h, a)
{{out}}
5.5
4.528728688116765
3.414171521474055
true
Run BASIC
bXsum = 1
for i = 1 to 10
sum = sum + i ' sum of 1 -> 10
bXsum = bXsum * i ' sum i * i
sum1i = sum1i + (1/i) ' sum 1/i
next
average = sum / 10
geometric = bXsum ^ (1/10)
harmonic = 10/sum1i
print "ArithmeticMean:";average
print "Geometric Mean:";geometric
print " Harmonic Mean:";harmonic
if (average >= geometric) and (geometric >= harmonic) then print "True" else print "False"
{{out}}
Arithmetic Mean:5.5
Geometric Mean:4.52872869
Harmonic Mean:3.41417132
True
Rust
fn main() {
let mut sum = 0.0;
let mut prod = 1;
let mut recsum = 0.0;
for i in 1..11{
sum += i as f32;
prod *= i;
recsum += 1.0/(i as f32);
}
let avg = sum/10.0;
let gmean = (prod as f32).powf(0.1);
let hmean = 10.0/recsum;
println!("Average: {}, Geometric mean: {}, Harmonic mean: {}", avg, gmean, hmean);
assert!( ( (avg >= gmean) && (gmean >= hmean) ), "Incorrect calculation");
}
{{out}}
Average: 5.5, Geometric mean:4.528729, Harmonic mean: 3.4141712
Scala
{{works with|Scala|2.8+}}
def arithmeticMean(n: Seq[Int]) = n.sum / n.size.toDouble
def geometricMean(n: Seq[Int]) = math.pow(n.foldLeft(1.0)(_*_), 1.0 / n.size.toDouble)
def harmonicMean(n: Seq[Int]) = n.size / n.map(1.0 / _).sum
var nums = 1 to 10
var a = arithmeticMean(nums)
var g = geometricMean(nums)
var h = harmonicMean(nums)
println("Arithmetic mean " + a)
println("Geometric mean " + g)
println("Harmonic mean " + h)
assert(a >= g && g >= h)
{{out}}
Arithmetic mean 5.5
Geometric mean 4.528728688116765
Harmonic mean 3.414171521474055
Scheme
{{Works with|Scheme|RRS}}
(define (a-mean l)
(/ (apply + l) (length l)))
(define (g-mean l)
(expt (apply * l) (/ (length l))))
(define (h-mean l)
(/ (length l) (apply + (map / l))))
(define (iota start stop)
(if (> start stop)
(list)
(cons start (iota (+ start 1) stop))))
(let* ((l (iota 1 10)) (a (a-mean l)) (g (g-mean l)) (h (h-mean l)))
(display a)
(display " >= ")
(display g)
(display " >= ")
(display h)
(newline)
(display (>= a g h))
(newline))
{{out}}
## Seed7
```seed7
$ include "seed7_05.s7i";
include "float.s7i";
const array float: numbers is [] (1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0);
const func proc: main is func
local
var float: number is 0.0;
var float: sum is 0.0;
var float: product is 1.0;
var float: reciprocalSum is 0.0;
begin
for number range numbers do
sum +:= number;
product *:= number;
reciprocalSum +:= 1.0 / number;
end for;
writeln("Arithmetic mean: " <& sum / flt(length(numbers)));
writeln("Geometric mean: " <& product ** (1.0 / flt(length(numbers))));
writeln("Harmonic mean: " <& flt(length(numbers)) / reciprocalSum);
end func;
{{out}}
Arithmetic mean: 5.5
Geometric mean: 4.528728961944580078125
Harmonic mean: 3.4141712188720703125
Sidef
func A(a) { a.sum / a.len }
func G(a) { a.prod.root(a.len) }
func H(a) { a.len / a.map{1/_}.sum }
The same thing, using hyper-operators:
func A(a) { a«+» / a.len }
func G(a) { a«*» ** (1/a.len) }
func H(a) { a.len / (a«/«1 «+») }
Calling the functions:
say("A(1,...,10) = ", A(1..10));
say("G(1,...,10) = ", G(1..10));
say("H(1,...,10) = ", H(1..10));
{{out}}
A(1,...,10) = 5.5
G(1,...,10) = 4.528728688116764762203309337195508793499
H(1,...,10) = 3.414171521474055006096734859775098225173
SQL
It may not be possible to calculate a geometric mean in a query, but the other two are easy enough.
--setup
create table averages (val integer);
insert into averages values (1);
insert into averages values (2);
insert into averages values (3);
insert into averages values (4);
insert into averages values (5);
insert into averages values (6);
insert into averages values (7);
insert into averages values (8);
insert into averages values (9);
insert into averages values (10);
-- calculate means
select
1/avg(1/val) as harm,
avg(val) as arith
from
averages;
{{out}}
HARM ARITH
---------- ----------
3.41417152 5.5
Smalltalk
{{works with|GNU Smalltalk}}
This extends the class Collection, so these three methods can be called over any kind of collection, it is enough the the objects of the collection understand +, *, raisedTo, reciprocal and /.
Collection extend
[
arithmeticMean
[
^ (self fold: [:a :b| a + b ]) / (self size)
]
geometricMean
[
^ (self fold: [:a :b| a * b]) raisedTo: (self size reciprocal)
]
harmonicMean
[
^ (self size) / ((self collect: [:x|x reciprocal]) fold: [:a :b| a + b ] )
]
]
|a|
a := #(1 2 3 4 5 6 7 8 9 10).
a arithmeticMean asFloat displayNl.
a geometricMean asFloat displayNl.
a harmonicMean asFloat displayNl.
((a arithmeticMean) >= (a geometricMean)) displayNl.
((a geometricMean) >= (a harmonicMean)) displayNl.
{{out}}
5.5
4.528728688116765
3.414171521474055
true
true
Stata
The command [http://www.stata.com/help.cgi?ameans ameans] prints the arithmetic, geometric and harmonic means, together with confidence intervals.
Variable | Type Obs Mean [95% Conf. Interval]
-------------+--------------------------------------------------------------- x | Arithmetic 10 5.5 3.334149 7.665851 | Geometric 10 4.528729 2.680672 7.650836 | Harmonic 10 3.414172 2.035664 10.57602
## Tcl
```tcl
proc arithmeticMean list {
set sum 0.0
foreach value $list { set sum [expr {$sum + $value}] }
return [expr {$sum / [llength $list]}]
}
proc geometricMean list {
set product 1.0
foreach value $list { set product [expr {$product * $value}] }
return [expr {$product ** (1.0/[llength $list])}]
}
proc harmonicMean list {
set sum 0.0
foreach value $list { set sum [expr {$sum + 1.0/$value}] }
return [expr {[llength $list] / $sum}]
}
set nums {1 2 3 4 5 6 7 8 9 10}
set A10 [arithmeticMean $nums]
set G10 [geometricMean $nums]
set H10 [harmonicMean $nums]
puts "A10=$A10, G10=$G10, H10=$H10"
if {$A10 >= $G10} { puts "A10 >= G10" }
if {$G10 >= $H10} { puts "G10 >= H10" }
{{out}}
A10=5.5, G10=4.528728688116765, H10=3.414171521474055
A10 >= G10
G10 >= H10
Ursala
#import std
#import flo
data = ari10(1.,10.) # arithmetic progression, length 10 with endpoints 1 and 10
a = mean data
g = exp mean ln* data
h = div/1. mean div/*1. data
#cast %eLbX
main = ^(~&,ordered not fleq) <a,g,h>
{{out}}
(
<5.500000e+00,4.528729e+00,3.414172e+00>,
true)
Vala
Most valac setups will need "-X -lm" added to the compile command to include the C math library.
double arithmetic(int[] list){
double mean;
double sum = 0;
foreach(int number in list){
sum += number;
} // foreach
mean = sum / list.length;
return mean;
} // end arithmetic mean
double geometric(int[] list){
double mean;
double product = 1;
foreach(int number in list){
product *= number;
} // foreach
mean = Math.pow(product, (1 / (double) list.length));
return mean;
} // end geometric mean
double harmonic(int[] list){
double mean;
double sum_inverse = 0;
foreach(int number in list){
sum_inverse += (1 / (double) number);
} // foreach
mean = (double) list.length / sum_inverse;
return mean;
} // end harmonic mean
public static void main(){
int[] list = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
double arithmetic_mean = arithmetic(list);
double geometric_mean = geometric(list);
double harmonic_mean = harmonic(list);
// should be 5.5
stdout.printf("Arithmetic mean: %s\n", arithmetic_mean.to_string());
// should be 4.528728688116765
stdout.printf("Geometric mean: %s\n", geometric_mean.to_string());
// should be 4.528728688116765
stdout.printf("Harmonic mean: %s\n", harmonic_mean.to_string());
}
{{out}}
Arithmetic mean: 5.5
Geometric mean: 4.5287286881167654
Harmonic mean: 3.4141715214740551
VBA
Uses Excel VBA.
Private Function arithmetic_mean(s() As Variant) As Double
arithmetic_mean = WorksheetFunction.Average(s)
End Function
Private Function geometric_mean(s() As Variant) As Double
geometric_mean = WorksheetFunction.GeoMean(s)
End Function
Private Function harmonic_mean(s() As Variant) As Double
harmonic_mean = WorksheetFunction.HarMean(s)
End Function
Public Sub pythagorean_means()
Dim s() As Variant
s = [{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}]
Debug.Print "A ="; arithmetic_mean(s)
Debug.Print "G ="; geometric_mean(s)
Debug.Print "H ="; harmonic_mean(s)
End Sub
{{out}}
A = 5,5
G = 4,52872868811677
H = 3,41417152147406
VBScript
Function arithmetic_mean(arr)
sum = 0
For i = 0 To UBound(arr)
sum = sum + arr(i)
Next
arithmetic_mean = sum / (UBound(arr)+1)
End Function
Function geometric_mean(arr)
product = 1
For i = 0 To UBound(arr)
product = product * arr(i)
Next
geometric_mean = product ^ (1/(UBound(arr)+1))
End Function
Function harmonic_mean(arr)
sum = 0
For i = 0 To UBound(arr)
sum = sum + (1/arr(i))
Next
harmonic_mean = (UBound(arr)+1) / sum
End Function
WScript.StdOut.WriteLine arithmetic_mean(Array(1,2,3,4,5,6,7,8,9,10))
WScript.StdOut.WriteLine geometric_mean(Array(1,2,3,4,5,6,7,8,9,10))
WScript.StdOut.WriteLine harmonic_mean(Array(1,2,3,4,5,6,7,8,9,10))
{{Out}}
5.5
4.52872868811677
3.41417152147406
Visual Basic .NET
{{trans|C#}}
Imports System.Runtime.CompilerServices
Module Module1
<Extension()>
Function Gmean(n As IEnumerable(Of Double)) As Double
Return Math.Pow(n.Aggregate(Function(s, i) s * i), 1.0 / n.Count())
End Function
<Extension()>
Function Hmean(n As IEnumerable(Of Double)) As Double
Return n.Count() / n.Sum(Function(i) 1.0 / i)
End Function
Sub Main()
Dim nums = From n In Enumerable.Range(1, 10) Select CDbl(n)
Dim a = nums.Average()
Dim g = nums.Gmean()
Dim h = nums.Hmean()
Console.WriteLine("Arithmetic mean {0}", a)
Console.WriteLine(" Geometric mean {0}", g)
Console.WriteLine(" Harmonic mean {0}", h)
Debug.Assert(a >= g AndAlso g >= h)
End Sub
End Module
{{out}}
Arithmetic mean 5.5
Geometric mean 4.52872868811677
Harmonic mean 3.41417152147406
XPL0
include c:\cxpl\codes;
func real Power(X, Y); \X raised to the Y power
real X, Y; \ (from StdLib.xpl)
return Exp(Y * Ln(X));
int N, Order;
real R, A, A1, G, G1, H, H1;
[A1:= 0.0; G1:= 1.0; H1:= 0.0;
Order:= true;
for N:= 1 to 10 do
[R:= float(N); \convert integer N to real R
A1:= A1 + R;
A:= A1/R; \arithmetic mean
G1:= G1 * R;
G:= Power(G1, 1.0/R); \geometric mean (Nth root of G1)
if G>A then Order:= false;
H1:= H1 + 1.0/R;
H:= R/H1; \harmonic mean
if H>G then Order:= false;
];
RlOut(0, A); CrLf(0);
RlOut(0, G); CrLf(0);
RlOut(0, H); CrLf(0);
if not Order then Text(0, "NOT ");
Text(0, "ALWAYS DECREASING ORDER
");
]
{{out}}
5.50000
4.52873
3.41417
ALWAYS DECREASING ORDER
zkl
ns:=T(1,2,3,4,5,6,7,8,9,10);
ns.sum(0.0)/ns.len(); // Arithmetic mean
ns.reduce('*,1.0).pow(1.0/ns.len()); // Geometric mean
ns.len().toFloat() / ns.reduce(fcn(p,n){ p + 1.0/n },0.0); // Harmonic mean
{{out}}
5.5
4.52873
3.41417
[[Category:Geometry]]