Averages/Pythagorean means
You are encouraged to solve this task according to the task description, using any language you may know.
Compute all three of the Pythagorean means of the set of integers 1 through 10.
Show that for this set of positive integers.
- The most common of the three means, the arithmetic mean, is the sum of the list divided by its length:
- The geometric mean is the th root of the product of the list:
- The harmonic mean is divided by the sum of the reciprocal of each item in the list:
C.f. Averages/Root mean square
ActionScript
<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));</lang>
Ada
pythagorean_means.ads: <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;</lang>
pythagorean_means.adb: <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;</lang>
example main.adb: <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;</lang>
ALGOL 68
<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))
)</lang> Lunix command:
a68g Averages_Pythagorean_means.a68 - 1 2 3 4 5 6 7 8 9 10
- Output:
c: 10.0000 s: 55.0000 p: 3628800.0000 r: 2.9290 Arithmetic mean = 5.5000 Geometric mean = 4.5287 Harmonic mean = 3.4142
APL
<lang APL>
arithmetic←{(+/⍵)÷⍴⍵}
geometric←{(×/⍵)*÷⍴⍵}
harmonic←{(⍴⍵)÷(+/÷⍵)}
x←⍳10
arithmetic x
5.5
geometric x
4.528728688
harmonic x
3.414171521 </lang>
AutoHotkey
<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
}</lang> Message box shows:
5.500000 4.528729 3.414172 True
AWK
<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;
}</lang>
BBC BASIC
The arithmetic and harmonic means use BBC BASIC's built-in array operations; only the geometric mean needs a loop. <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())
</lang>
- Output:
Arithmetic mean = 5.5 Geometric mean = 4.52872869 Harmonic mean = 3.41417152
C
<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;
}</lang>
C++
<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 ;
}</lang>
- Output:
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.
<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 / i);
}
}
}</lang>
- Output:
Arithmetic mean 5.5 Geometric mean 4.52872868811677 Harmonic mean 3.41417152147406
Common Lisp
<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)))</lang>
Clojure
<lang lisp>(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))</lang>
D
<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);
}</lang>
- Output:
0.9891573712076470036 4.5287286881167647619 5.5000000000000000000
Delphi
<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.</lang>
E
Given that we're defining all three together, it makes sense to express their regularities:
<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 })</lang>
<lang e>? A(1..10)
- value: 5.5
? G(1..10)
- value: 4.528728688116765
? H(1..10)
- value: 3.414171521474055</lang>
Elixir
<lang elixir> defmodule Means do
def arithmetic(list) do Enum.sum(list) / Enum.count(list) end def geometric(list) do :math.pow(Enum.reduce(list, &(&1 * &2)), 1 / Enum.count(list)) end def harmonic(list) do 1 / arithmetic(Enum.map(list, &(1 / &1))) end
end
IO.puts "Arithmetic mean: #{am = Means.arithmetic(1..10)}" IO.puts "Geometric mean: #{gm = Means.geometric(1..10)}" IO.puts "Harmonic mean: #{hm = Means.harmonic(1..10)}" IO.puts "(#{am} >= #{gm} >= #{hm}) is #{am >= gm and gm >= hm}" </lang>
- Output:
Arithmetic mean: 5.5 Geometric mean: 4.528728688116765 Harmonic mean: 3.414171521474055 (5.5 >= 4.528728688116765 >= 3.414171521474055) is true
Erlang
<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). </lang>
- Output:
Arithmetic Mean 5.5 Geometric Mean 4.528728688116765 Harmonic Mean 3.414171521474055
ERRE
<lang> 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 </lang>
Euler Math Toolbox
<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
</lang>
Alternatively, e.g.,
<lang Euler Math Toolbox> >function G(x) := prod(x)^(1/length(x)) </lang>
Euphoria
<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)})</lang>
- Output:
Arithmetic: 5.5 Geometric: 4.52873 Harmonic: 3.41417 Arithmetic>=Geometric>=Harmonic: true
F#
<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)</lang>
Factor
<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 / ;</lang>
( scratchpad ) 10 [1,b] [ a-mean ] [ g-mean ] [ h-mean ] tri
"%f >= %f >= %f\n" printf
5.500000 >= 4.528729 >= 3.414172
Fantom
<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")
}
} </lang>
Forth
<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</lang>
Fortran
<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</lang>
FunL
<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, (>=)) )</lang>
- Output:
Arithmetic: 11/2 or 5.5 Geometric: 4.528728688116765 Harmonic: 25200/7381 or 3.414171521474055 true
GAP
<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</lang>
Go
<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)
}</lang>
- Output:
A: 5.5 G: 4.528728688116765 H: 3.414171521474055 A >= G >= H: true
Groovy
Solution: <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()
}</lang>
Test: <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}
"""</lang>
- Output:
list: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] A: 5.5 G: 4.528728688116765 H: 3.4141715214
Haskell
The 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.
<lang haskell>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))</lang>
HicEst
<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)</lang> ! A=5.5; G=4.528728688; H=3.414171521; Result = 1;
Icon and Unicon
<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 </lang>
numbers:amean, numbers:gmean, and numbers:hmean are shown below: <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</lang>
- Output:
#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
J
Solution: <lang j>amean=: +/ % # gmean=: # %: */ hmean=: amean&.:%</lang>
Example Usage: <lang j> (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</lang>
Note that gmean could have instead been defined as mean under logarithm, for example:
<lang j>gmean=:amean&.:^.</lang>
Java
<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));
}
}</lang>
- Output:
A = 5.500000 G = 4.528729 H = 3.414172 A >= G is true, G >= H is true
JavaScript
,
<lang javascript>function arithmetic_mean(ary) {
var sum = ary.reduce(function(s,x) {return (s+x)}, 0);
return (sum / ary.length);
}
function geometic_mean(ary) {
var product = ary.reduce(function(s,x) {return (s*x)}, 1);
return Math.pow(product, 1/ary.length);
}
function harmonic_mean(ary) {
var sum_of_inv = ary.reduce(function(s,x) {return (s + 1/x)}, 0);
return (ary.length / sum_of_inv);
}
var ary = [1,2,3,4,5,6,7,8,9,10]; var A = arithmetic_mean(ary); var G = geometic_mean(ary); var H = harmonic_mean(ary);
print("is A >= G >= H ? " + (A >= G && G >= H ? "yes" : "no"));</lang>
jq
<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] )" )
</lang>
- Output:
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. <lang Julia>amean(A) = sum(A)/length(A)
gmean(A) = prod(A)^(1/length(A))
hmean(A) = length(A)/sum(1./A)</lang>
- Output:
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
Lasso
<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)</lang>
- Output:
5.500000 4.528729 3.414172
Liberty BASIC
<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
</lang>
Logo
<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</lang>
Lua
<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 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)</lang>
Maple
<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 ); </lang>
- Output:
Arithmeticmean, Geometricmean, Harmonicmean := 5.50000000000000, 4.52872868811677, 3.41417152147406 true
Mathematica
<lang Mathematica>Print["{Arithmetic Mean, Geometric Mean, Harmonic Mean} = ",
N@Through[{Mean, GeometricMean, HarmonicMean}[Range@10]]]</lang>
- Output:
{Arithmetic Mean, Geometric Mean, Harmonic Mean} = {5.5,4.52873,3.41417}
MATLAB
<lang MATLAB>function [A,G,H] = pythagoreanMeans(list)
A = mean(list); G = geomean(list); H = harmmean(list);
end</lang>
A solution that works for both, Matlab and Octave, is this
<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</lang>
Solution: <lang MATLAB>>> [A,G,H]=pythagoreanMeans((1:10))
A =
5.500000000000000
G =
4.528728688116765
H =
3.414171521474055</lang>
Maxima
<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 */</lang>
MUMPS
<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</lang>
NetRexx
<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
</lang>
- Output:
Arithmetic = 5.5, Geometric = 4.528728688116765, Harmonic = 3.4141715214740550062
Nim
<lang nim>import math, sequtils, future
proc amean(num): float =
sum(num) / float(len(num))
proc gmean(num): float =
result = 1 for n in num: result *= n result = pow(result, 1.0 / float(num.len))
proc hmean(num): 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)</lang>
- Output:
5.5000000000000000e+00 4.5287286881167654e+00 3.4141715214740551e+00
Oberon-2
Oxford Oberon-2 <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.
</lang>
- Output:
A(1 .. 10): 5.50000000000 G(1 .. 10): 4.52872868812 H(1 .. 10): 3.41417152147
Objeck
<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;
}
}</lang>
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
<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)
- </lang>
- Output:
means (Array.init 10 (function i -> (float_of_int (i+1)))) ;; (* (5.5, 4.5287286881167654, 3.4141715214740551) *)
Another implementation using Array.fold_left instead of a for loop:
<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)
- </lang>
Octave
<lang Octave>
A = mean(list); % arithmetic mean G = mean(list,'g'); % geometric mean H = mean(list,'a'); % harmonic mean
</lang>
See also Matlab implementation #MATLAB
Oforth
<lang Oforth>func: A(l) { l avg } func: G(l) { l prod l size inv powf } func: H(l) { l size l map(#inv) sum / }
func: averages { | g |
"Geometric mean : " print G(10 seq) dup println ->g "Arithmetic mean : " print A(10 seq) dup print g >= ifTrue: [ " ==> A >= G" println ] "Harmonic mean : " print H(10 seq) dup print g <= ifTrue: [ " ==> G >= H" println ]
}</lang>
- Output:
Geometric mean : 4.52872868811677 Arithmetic mean : 5.5 ==> A >= G Harmonic mean : 3.41417152147406 ==> G >= H
ooRexx
<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
</lang>
Oz
<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</lang>
PARI/GP
General implementations: <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)]</lang>
Specific to the first n positive integers: <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]</lang>
These are, asymptotically, n/2, n/e, and n/log n.
Pascal
See Delphi
Perl
<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;</lang>
Perl 6
<lang Perl6>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); </lang>
- Output:
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) <lang Phix>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")})</lang>
- Output:
Arithmetic: 5.5 Geometric: 4.528728688 Harmonic: 3.414171521 Arithmetic>=Geometric>=Harmonic: true
PicoLisp
<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 ) ) )</lang>
- Output:
Arithmetic mean: 5.500000 Geometric mean: 4.528729 Harmonic mean: 3.414172
PL/I
<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);
/* 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'); </lang> Results:
AVERAGE= 5.50000E+0000; GEOMETRIC= 4.52873E+0000; HARMONIC= 3.41417E+0000;
PostScript
<lang> /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 </lang>
- Output:
Arithmetic Mean : 5.5 Geometric Mean : 4.52873 Harmonic Mean : 3.41417
<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 </lang>
PowerShell
<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)"</lang>
- Output:
Arithmetic mean: A = 5.5 Geometric mean: G = 4.52872868811676 Harmonic mean: H = 3.41417152147405 Is A >= G ? True Is G >= H ? True
PureBasic
<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()</lang>
Python
<lang Python>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 ) </lang>
- Output:
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 <lang R>
x <- 1:10
</lang> Arithmetic mean <lang R> a <- sum(x)/length(x)
</lang> or <lang R> a <- mean(x) </lang>
The geometric mean <lang R> g <- prod(x)^(1/length(x)) </lang>
The harmonic mean (no error checking that ) <lang R> h <- length(x)/sum(1/x) </lang>
Then:
<lang R> a > g </lang>
and
<lang R> g > h </lang>
give both
[1] TRUE
Racket
<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)) </lang>
- Output:
5 1/2 4.528728688116765 3 3057/7381 #t
REXX
REXX doesn't have a POW function, so an IROOT (integer root) function is included here.
Coding note: while the do loop flow looks nice, it took a bit of work to get exactly right,
and doesn't lend itself to being updated easily.
<lang rexx>/*REXX program to compute and display Pythagorean means [Amean, Gmean, Hmean].*/
parse arg n . /*obtain the optional argument from CL.*/
if n== then n=10 /*None specified? Then assume default.*/
sum=0 /*░░░░░░░░░░░░░░░░░░compute Amean [Arithmetic mean]░░░░░░*/
do a=1 for n /*populate the array and calculate sum.*/
@.a=a /*populate the stemmed array @. */
sum=sum + @.a /*compute the sum of all the elements. */
end /*a*/
Amean=sum/n /*calculate the arithmetic mean. */ say 'Amean =' Amean /*display " " " */ prod=1 /*░░░░░░░░░░░░░░░░░░compute Gmean [Geometric mean]░░░░░░░*/
do g=1 for n
prod=prod * @.g /*compute the product of all elements. */
end /*g*/
Gmean=Iroot(prod,n) /*calculate the geometric mean. */ say 'Gmean =' Gmean /*display " " " */ rsum=0 /*░░░░░░░░░░░░░░░░░░compute Hmean [Harmonic mean]░░░░░░░░*/
do r=1 for n
rsum=rsum + 1/@.r /*compute the sum of the reciprocals. */
end /*r*/
Hmean=n/rsum /*calculate the harmonic mean. */ say 'Hmean =' Hmean /*display " " " */ 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 then return x /*handle special case of zero and unity*/ if y=0 then return 1 /* " " " " a zero root.*/ if y=1 then return x /* " " " " a unity root.*/ if x<0 & y//2==0 then do /*check for an illegal combination. */
say; say '*** error! *** (from Iroot):'; say
say 'root' y "can't be even if first argument is < 0."
say; return '[n/a]' /*return a "not applicable" text.*/
end
x=abs(x); y=abs(y); m=y-1 /*use the absolute value for X and Y. */ digO=digits() /*save original accuracy (decimal digs)*/ a=digO+5 /*use an extra five digs " " */ g=(x+1)/y**y /*use this as the first guesstimate. */ numeric fuzz 3 /*use three fuzz digits for comparisons*/ d=5 /*Start with 5 digits accuracy. When the digits is large, */
/*CPU time is wasted when the guess isn't close to the root.*/
do forever /* ◄──────────────────┐ keep plugging as digits are increased*/
d=min(d+d,a) /* │ limit the digits to original digs+5. */
numeric digits d /* │ keep increasing the accuracy. */
old=. /* │ define the old (guess). */
/* │ */
do forever /* ◄─────────────┐ │ keep plugging at the Yth root. */
_=(m*g**y+x)/y/g**m /* │ │ this is the nitty─gritty stuff. */
if _=g | _=old then leave /* │ │ are we close enough yet ? */
old=g; g=_ /* │ │ save guess to old); set new guess. */
end /*forever ►─────────────┘ │ */
/* │ */
if d==a then leave /* │ are we at the desired accuracy ? */
end /*forever ►────────────────┘ */
_=g*sign(ox); if oy<0 then _=1/_ /*adjust for original X sing; neg. root*/ numeric digits digO; return _/1 /*normalize to original decimal digits.*/</lang>
- Output:
Amean = 5.5 Gmean = 4.52872869 Hmean = 3.41417153
Ruby
<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)</lang>
- Output:
5.5 4.528728688116765 3.414171521474055 true
Run BASIC
<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"</lang>
- Output:
Arithmetic Mean:5.5 Geometric Mean:4.52872869 Harmonic Mean:3.41417132 True
Scala
<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)</lang>
- Output:
Arithmetic mean 5.5 Geometric mean 4.528728688116765 Harmonic mean 3.414171521474055
Scheme
<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))</lang>
- Output:
<lang>11/2 >= 4.528728688116765 >= 25200/7381
- t</lang>
Seed7
<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;</lang>
- Output:
Arithmetic mean: 5.5 Geometric mean: 4.528728961944580078125 Harmonic mean: 3.4141712188720703125
Sidef
<lang ruby>func A(a) { a.sum / a.len }; func G(a) { a.prod.root(a.len) }; func H(a) { a.len / a.map{1/_}.sum };
say("A(1,...,10) = ", A(1..10)); say("G(1,...,10) = ", G(1..10)); say("H(1,...,10) = ", H(1..10));</lang>
- Output:
A(1,...,10) = 5.5 G(1,...,10) = 4.528728688116764762203309337195508793499 H(1,...,10) = 3.414171521474055006096734859775098225173
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 /.
<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.</lang>
- Output:
5.5 4.528728688116765 3.414171521474055 true true
Tcl
<lang 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" }</lang>
- Output:
A10=5.5, G10=4.528728688116765, H10=3.414171521474055 A10 >= G10 G10 >= H10
Ursala
<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></lang>
- Output:
( <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.
<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()); } </lang>
- Output:
Arithmetic mean: 5.5 Geometric mean: 4.5287286881167654 Harmonic mean: 3.4141715214740551
XPL0
<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 "); ]</lang>
- Output:
5.50000
4.52873
3.41417
ALWAYS DECREASING ORDER
zkl
<lang zkl>var 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</lang>
- Output:
5.5 4.52873 3.41417
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