Averages/Arithmetic mean: Difference between revisions
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A little more elaborate that the task requires. The function "mean" fulfills the task of "a program to find the mean." As a Go idiom, it returns an ok value of true if result m is valid. An ok value of false means the input "vector" (a Go slice) was empty. The fancy accuracy preserving algorithm is a little more than was called more. The program main is a test program demonstrating the ok idiom and several data cases. |
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<lang go>package main |
<lang go>package main |
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Revision as of 19:41, 18 June 2013
You are encouraged to solve this task according to the task description, using any language you may know.
Write a program to find the mean (arithmetic average) of a numeric vector. In case of a zero-length input, since the mean of an empty set of numbers is ill-defined, the program may choose to behave in any way it deems appropriate, though if the programming language has an established convention for conveying math errors or undefined values, it's preferable to follow it.
6502 Assembly
Called as a subroutine (i.e., JSR ArithmeticMean), this calculates the integer average of up to 255 8-bit unsigned integers. The address of the beginning of the list of integers is in the memory location ArrayPtr and the number of integers is in the memory location NumberInts. The arithmetic mean is returned in the memory location ArithMean.
<lang 6502asm>ArithmeticMean: PHA TYA PHA ;push accumulator and Y register onto stack
LDA #0
STA Temp
STA Temp+1 ;temporary 16-bit storage for total
LDY NumberInts BEQ Done ;if NumberInts = 0 then return an average of zero
DEY ;start with NumberInts-1 AddLoop: LDA (ArrayPtr),Y CLC ADC Temp STA Temp LDA Temp+1 ADC #0 STA Temp+1 DEY CPY #255 BNE AddLoop
LDY #-1 DivideLoop: LDA Temp SEC SBC NumberInts STA Temp LDA Temp+1 SBC #0 STA Temp+1 INY BCS DivideLoop
Done: STY ArithMean ;store result here PLA ;restore accumulator and Y register from stack TAY PLA RTS ;return from routine</lang>
ACL2
<lang Lisp>(defun mean-r (xs)
(if (endp xs)
(mv 0 0)
(mv-let (m j)
(mean-r (rest xs))
(mv (+ (first xs) m) (+ j 1)))))
(defun mean (xs)
(if (endp xs)
0
(mv-let (n d)
(mean-r xs)
(/ n d))))</lang>
ActionScript
<lang ActionScript>function mean(vector:Vector.<Number>):Number { var sum:Number = 0; for(var i:uint = 0; i < vector.length; i++) sum += vector[i]; return vector.length == 0 ? 0 : sum / vector.length; }</lang>
Ada
This example shows how to pass a zero length vector as well as a larger vector. <lang ada>with Ada.Float_Text_Io; use Ada.Float_Text_Io; with Ada.Text_IO; use Ada.Text_IO;
procedure Mean_Main is
type Vector is array(Positive range <>) of Float;
function Mean(Item : Vector) return Float is
Sum : Float := 0.0;
Result : Float := 0.0;
begin
for I in Item'range loop
Sum := Sum + Item(I);
end loop;
if Item'Length > 0 then
Result := Sum / Float(Item'Length);
end if;
return Result;
end Mean;
A : Vector := (3.0, 1.0, 4.0, 1.0, 5.0, 9.0);
begin
Put(Item => Mean(A), Fore => 1, Exp => 0); New_Line; -- test for zero length vector Put(Item => Mean(A(1..0)), Fore => 1, Exp => 0); New_Line;
end Mean_Main;</lang> Output:
3.83333 0.00000
ALGOL 68
<lang algol68>PROC mean = (REF[]REAL p)REAL:
- Calculates the mean of qty REALs beginning at p. #
IF LWB p > UPB p THEN 0.0 ELSE REAL total := 0.0; FOR i FROM LWB p TO UPB p DO total +:= p[i] OD; total / (UPB p - LWB p + 1) FI;
main:(
[6]REAL test := (1.0, 2.0, 5.0, -5.0, 9.5, 3.14159); print((mean(test),new line))
)</lang>
AmigaE
Because of the way Amiga E handles floating point numbers, the passed list/vector must contain all explicitly floating point values (e.g., you need to write "1.0", not "1") <lang amigae>PROC mean(l:PTR TO LONG)
DEF m, i, ll ll := ListLen(l) IF ll = 0 THEN RETURN 0.0 m := 0.0 FOR i := 0 TO ll-1 DO m := !m + l[i] m := !m / (ll!)
ENDPROC m
PROC main()
DEF s[20] : STRING
WriteF('mean \s\n',
RealF(s,mean([1.0, 2.0, 3.0, 4.0, 5.0]), 2))
ENDPROC</lang>
AutoHotkey
<lang autohotkey>i = 10 Loop, % i {
Random, v, -3.141592, 3.141592 list .= v "`n" sum += v
} MsgBox, % i ? list "`nmean: " sum/i:0</lang>
AWK
<lang awk># work around a gawk bug in the length extended use:
- so this is a more non-gawk compliant way to get
- how many elements are in an array
function elength(v) {
l=0 for(el in v) l++ return l
}
function mean(v) {
if (elength(v) < 1) { return 0 }
sum = 0
for(i=0; i < elength(v); i++) {
sum += v[i]
}
return sum/elength(v)
}
BEGIN {
# fill a vector with random numbers
for(i=0; i < 10; i++) {
vett[i] = rand()*10
}
print mean(vett)
}</lang>
APL
<lang apl> X←3 1 4 1 5 9
(+/X)÷⍴X
3.833333333</lang>
BASIC
Assume the numbers are in an array named "nums". <lang qbasic>mean = 0 sum = 0; FOR i = LBOUND(nums) TO UBOUND(nums)
sum = sum + nums(i);
NEXT i size = UBOUND(nums) - LBOUND(nums) + 1 PRINT "The mean is: "; IF size <> 0 THEN
PRINT (sum / size)
ELSE
PRINT 0
END IF</lang>
BBC BASIC
To calculate the mean of an array: <lang BBC BASIC>
REM specific functions for the array/vector types
REM Byte Array
DEF FN_Mean_Arithmetic&(n&())
= SUM(n&()) / (DIM(n&(),1)+1)
REM Integer Array
DEF FN_Mean_Arithmetic%(n%())
= SUM(n%()) / (DIM(n%(),1)+1)
REM Float 40 array
DEF FN_Mean_Arithmetic(n())
= SUM(n()) / (DIM(n(),1)+1)
REM A String array
DEF FN_Mean_Arithmetic$(n$())
LOCAL I%, S%, sum, Q%
S% = DIM(n$(),1)
FOR I% = 0 TO S%
Q% = TRUE
ON ERROR LOCAL Q% = FALSE
IF Q% sum += EVAL(n$(I%))
NEXT
= sum / (S%+1)
REM Float 64 array
DEF FN_Mean_Arithmetic#(n#())
= SUM(n#()) / (DIM(n#(),1)+1)
</lang> Michael Hutton 14:02, 29 May 2011 (UTC)
Befunge
This example can't deal with null inputs (i.e., blank input, or first input is 0 (zero)). <lang befunge>0001>p&: #v_$::01g/.@
^10+1g10+<
Enter 0 (zero) to finish.</lang>
Bracmat
Here are two solutions. The first uses a while loop, the second scans the input by backtracking. <lang bracmat> (mean1=
sum length n
. 0:?sum:?length
& whl
' ( !arg:%?n ?arg
& 1+!length:?length
& !n+!sum:?sum
)
& !sum*!length^-1
);
(mean2=
sum length n
. 0:?sum:?length
& !arg
: ?
( #%@?n
& 1+!length:?length
& !n+!sum:?sum
& ~
)
?
| !sum*!length^-1
); </lang> To test with a list of all numbers 1 .. 999999: <lang bracmat> ( :?test & 1000000:?Length & whl'(!Length+-1:?Length:>0&!Length !test:?test) & out$mean1$!test & out$mean2$!test )</lang>
Brainf***
This code is an infinite loop if the average isn't a whole number. I don't have the time, can someone fix it to work with all numbers, not just single-digit numbers? <lang bf>>,[-<+>>+<],<[->-<]>[-->+<]>.</lang>
Brat
<lang brat>mean = { list |
true? list.empty?, 0, { list.reduce(0, :+) / list.length }
}
p mean 1.to 10 #Prints 5.5</lang>
Burlesque
<lang burlesque> blsq ) {1 2 2.718 3 3.142}av 2.372 blsq ) {}av NaN </lang>
C
Compute mean of a double array of given length. If length is zero, does whatever 0/0 does (usually means returning NaN).
<lang c>#include <stdio.h>
double mean(double *v, int len) { double sum = 0; int i; for (i = 0; i < len; i++) sum += v[i]; return sum / len; }
int main(void) { double v[] = {1, 2, 2.718, 3, 3.142}; int i, len; for (len = 5; len >= 0; len--) { printf("mean["); for (i = 0; i < len; i++) printf(i ? ", %g" : "%g", v[i]); printf("] = %g\n", mean(v, len)); }
return 0;
}</lang>
- Output:
mean[1, 2, 2.718, 3, 3.142] = 2.372 mean[1, 2, 2.718, 3] = 2.1795 mean[1, 2, 2.718] = 1.906 mean[1, 2] = 1.5 mean[1] = 1 mean[] = -nan
C#
<lang csharp>using System; using System.Linq;
class Program {
static void Main()
{
Console.WriteLine(new[] { 1, 2, 3 }.Average());
}
}</lang>
Alternative version (not using the built-in function): <lang csharp>using System;
class Program {
static void Main(string[] args)
{
double average = 0;
double[] numArray = { 1, 2, 3, 4, 5 };
average = Average(numArray);
Console.WriteLine(average); // Output is 3
// Alternative use
average = Average(1, 2, 3, 4, 5);
Console.WriteLine(average); // Output is still 3
Console.ReadLine();
}
static double Average(params double[] nums)
{
double d = 0;
foreach (double num in nums)
d += num;
return d / nums.Length;
}
}</lang>
C++
<lang cpp>#include <vector>
double mean(const std::vector<double>& numbers) {
if (numbers.size() == 0)
return 0;
double sum = 0;
for (std::vector<double>::iterator i = numbers.begin(); i != numbers.end(); i++)
sum += *i;
return sum / numbers.size();
}</lang>
Shorter (and more idiomatic) version:
<lang cpp>#include <vector>
- include <algorithm>
double mean(const std::vector<double>& numbers) {
if (numbers.empty())
return 0;
return std::accumulate(numbers.begin(), numbers.end(), 0.0) / numbers.size();
}</lang>
Idiomatic version templated on any kind of iterator:
<lang cpp>#include <iterator>
- include <algorithm>
template <typename Iterator> double mean(Iterator begin, Iterator end) {
if (begin == end)
return 0;
return std::accumulate(begin, end, 0.0) / std::distance(begin, end);
}</lang>
Chef
<lang Chef>Mean.
Chef has no way to detect EOF, so rather than interpreting some arbitrary number as meaning "end of input", this program expects the first input to be the sample size. Pass in the samples themselves as the other inputs. For example, if you wanted to compute the mean of 10, 100, 47, you could pass in 3, 10, 100, and 47. To test the "zero-length vector" case, you need to pass in 0.
Ingredients. 0 g Sample Size 0 g Counter 0 g Current Sample
Method. Take Sample Size from refrigerator. Put Sample Size into mixing bowl. Fold Counter into mixing bowl. Put Current Sample into mixing bowl. Loop Counter. Take Current Sample from refrigerator. Add Current Sample into mixing bowl. Endloop Counter until looped. If Sample Size. Divide Sample Size into mixing bowl. Put Counter into 2nd mixing bowl. Fold Sample Size into 2nd mixing bowl. Endif until ifed. Pour contents of mixing bowl into baking dish.
Serves 1.</lang>
Clojure
<lang lisp>(defn mean [sq]
(let [length (count sq)]
(if (zero? length)
0
(/ (reduce + sq) length)))
)</lang>
Cobra
<lang cobra> class Rosetta def mean(ns as List<of number>) as number if ns.count == 0 return 0 else sum = 0.0 for n in ns sum += n return sum / ns.count
def main print "mean of [[]] is [.mean(List<of number>())]" print "mean of 1,2,3,4 is [.mean([1.0,2.0,3.0,4.0])]" </lang>
Output:
mean of [] is 0 mean of [1, 2, 3, 4] is 2.5
CoffeeScript
<lang coffeescript> mean = (array) ->
return 0 if array.length is 0 sum = array.reduce (s,i,0) -> s += i sum / array.length
alert mean [1] </lang>
Common Lisp
With Reduce
<lang lisp>(defun mean (&rest sequence)
(if (null sequence)
nil
(/ (reduce #'+ sequence) (length sequence))))</lang>
With Loop <lang lisp>(defun mean (list)
(unless (null list)
(/ (loop for i in list sum i)
(length list))))</lang>
D
Imperative Version
<lang d>import std.stdio;
real mean(Range)(Range r) {
real sum = 0.0; int count;
foreach (item; r) {
sum += item;
count++;
}
if (count == 0)
return 0.0;
else
return sum / count;
}
void main() {
int[] data;
writeln("mean: ", data.mean());
data = [3, 1, 4, 1, 5, 9];
writeln("mean: ", data.mean());
}</lang>
- Output:
mean: 0 mean: 3.83333
More Functional Version
Same output. <lang d>import std.stdio, std.algorithm, std.range;
auto mean(Range)(Range r) {
auto len = r.walkLength();
return len == 0 ? 0.0 : reduce!q{a + b}(0.0L, r) / len;
}
void main() {
int[] data;
writeln("mean: ", data.mean());
data = [3, 1, 4, 1, 5, 9];
writeln("mean: ", data.mean());
}</lang>
More Precise Version
A (naive?) version that tries to minimize precision loss: <lang d>import std.stdio, std.conv, std.algorithm, std.math, std.traits;
CommonType!(T, real) mean(T)(T[] n ...) if (isNumeric!(T)) {
alias CommonType!(T, real) E;
auto num = n.dup;
schwartzSort!(abs, "a > b")(num);
return reduce!q{a+b}(0.0L, map!(to!E)(num)) / max(1, num.length);
}
void main() {
writefln("%8.5f", mean((int[]).init));
writefln("%8.5f", mean( 0, 3, 1, 4, 1, 5, 9, 0));
writefln("%8.5f", mean([-1e20, 3, 1, 4, 1, 5, 9, 1e20]));
}</lang>
- Output:
0.00000 2.87500 2.87500
Delphi
<lang Delphi>program AveragesArithmeticMean;
{$APPTYPE CONSOLE}
uses Types;
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;
begin
Writeln(Mean(TDoubleDynArray.Create())); Writeln(Mean(TDoubleDynArray.Create(1,2,3,4,5)));
end.</lang>
E
Slightly generalized to support any object that allows iteration.
<lang e>def meanOrZero(numbers) {
var count := 0
var sum := 0
for x in numbers {
sum += x
count += 1
}
return sum / 1.max(count)
}</lang>
Elena
<lang elena>#define std'basic'*.
- define std'patterns'*.
- define std'dictionary'*.
- class MeanAction
{
#field theValue.
#field theCount.
#role Empty
{
#method save : aWriter = 0 save:aWriter.
#method evaluate : aValue
[
theValue := Real::0.
theCount := Integer::0.
#shift.
self evaluate:aValue.
]
}
#initializer
[
#shift Empty.
]
#method save : aWriter = (theValue / theCount) save:aWriter.
#method evaluate : aValue
[
theCount += 1.
theValue += aValue.
]
#method start : aPattern
[
aPattern run:self.
^ Real64Value::self.
]
}
- symbol Program =
[
'program'Output << MeanAction start:Scan::(1, 2, 3, 4, 5, 6, 7, 8).
].</lang>
Emacs Lisp
<lang lisp> (defun mean (lst)
(/ (float (apply '+ lst)) (length lst))) (mean '(1 2 3 4))</lang>
Erlang
<lang erlang>mean([]) -> 0; mean(L) -> lists:sum(L)/erlang:length(L).</lang>
Euphoria
<lang Euphoria>function 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
sequence test test = {1.0, 2.0, 5.0, -5.0, 9.5, 3.14159} ? mean(test)</lang>
Factor
<lang factor>USING: math math.statistics ;
- arithmetic-mean ( seq -- n )
[ 0 ] [ mean ] if-empty ;</lang>
Tests:
<lang factor>( scratchpad ) { 2 3 5 } arithmetic-mean >float 3.333333333333333</lang>
Fantom
<lang fantom> class Main {
static Float average (Float[] nums)
{
if (nums.size == 0) return 0.0f
Float sum := 0f
nums.each |num| { sum += num }
return sum / nums.size.toFloat
}
public static Void main ()
{
[[,], [1f], [1f,2f,3f,4f]].each |Float[] i|
{
echo ("Average of $i is: " + average(i))
}
}
} </lang>
Fish
<lang Fish>!vl0=?vl1=?vl&! v< +<>0n; >n; >l1)?^&,n;</lang> Must be called with the values pre-populated on the stack, which can be done in the fish.py interpreter with the -v switch:
fish.py mean.fish -v 10 100 47 207.4
which generates:
91.1
Forth
<lang forth>: fmean ( addr n -- f )
0e dup 0= if 2drop exit then tuck floats bounds do i f@ f+ 1 floats +loop 0 d>f f/ ;
create test 3e f, 1e f, 4e f, 1e f, 5e f, 9e f, test 6 fmean f. \ 3.83333333333333</lang>
Fortran
In ISO Fortran 90 or later, use the SUM intrinsic, the SIZE intrinsic and the MAX intrinsic (to avoid divide by zero): <lang fortran>real, target, dimension(100) :: a = (/ (i, i=1, 100) /) real, dimension(5,20) :: b = reshape( a, (/ 5,20 /) ) real, pointer, dimension(:) :: p => a(2:1) ! pointer to zero-length array real :: mean, zmean, bmean real, dimension(20) :: colmeans real, dimension(5) :: rowmeans
mean = sum(a)/size(a) ! SUM of A's elements divided by SIZE of A mean = sum(a)/max(size(a),1) ! Same result, but safer code
! MAX of SIZE and 1 prevents divide by zero if SIZE == 0 (zero-length array)
zmean = sum(p)/max(size(p),1) ! Here the safety check pays off. Since P is a zero-length array,
! expression becomes "0 / MAX( 0, 1 ) -> 0 / 1 -> 0", rather than "0 / 0 -> NaN"
bmean = sum(b)/max(size(b),1) ! multidimensional SUM over multidimensional SIZE
rowmeans = sum(b,1)/max(size(b,2),1) ! SUM elements in each row (dimension 1)
! dividing by the length of the row, which is the number of columns (SIZE of dimension 2)
colmeans = sum(b,2)/max(size(b,1),1) ! SUM elements in each column (dimension 2)
! dividing by the length of the column, which is the number of rows (SIZE of dimension 1)</lang>
F#
The following computes the running mean using a tail-recursive approach. If we just sum all the values then divide by the number of values then we will suffer from overflow problems for large lists. See wikipedia about the moving average computation. <lang fsharp>let avg (a:float) (v:float) n =
a + (1. / ((float n) + 1.)) * (v - a)
let mean_series list =
let a, _ = List.fold_left (fun (a, n) h -> avg a (float h) n, n + 1) (0., 0) list in a</lang>
Checking this:
> mean_series [1; 8; 2; 8; 1; 7; 1; 8; 2; 7; 3; 6; 1; 8; 100] ;; val it : float = 10.86666667 > mean_series [] ;; val it : float = 0.0
We can also make do with the built-in List.average function
List.average [4;1;7;5;8;4;5;2;1;5;2;5]
GAP
<lang gap>Mean := function(v)
local n; n := Length(v); if n = 0 then return 0; else return Sum(v)/n; fi;
end;
Mean([3, 1, 4, 1, 5, 9]);
- 23/6</lang>
Go
A little more elaborate that the task requires. The function "mean" fulfills the task of "a program to find the mean." As a Go idiom, it returns an ok value of true if result m is valid. An ok value of false means the input "vector" (a Go slice) was empty. The fancy accuracy preserving algorithm is a little more than was called more. The program main is a test program demonstrating the ok idiom and several data cases.
<lang go>package main
import (
"fmt" "math"
)
func mean(v []float64) (m float64, ok bool) {
if len(v) == 0 {
return
}
// an algorithm that attempts to retain accuracy
// with widely different values.
var parts []float64
for _, x := range v {
var i int
for _, p := range parts {
sum := p + x
var err float64
switch ax, ap := math.Abs(x), math.Abs(p); {
case ax < ap:
err = x - (sum - p)
case ap < ax:
err = p - (sum - x)
}
if err != 0 {
parts[i] = err
i++
}
x = sum
}
parts = append(parts[:i], x)
}
var sum float64
for _, x := range parts {
sum += x
}
return sum / float64(len(v)), true
}
func main() {
for _, v := range [][]float64{
[]float64{}, // mean returns ok = false
[]float64{math.Inf(1), math.Inf(1)}, // answer is +Inf
// answer is NaN, and mean returns ok = true, indicating NaN
// is the correct result
[]float64{math.Inf(1), math.Inf(-1)},
[]float64{3, 1, 4, 1, 5, 9},
// large magnitude numbers cancel. answer is mean of small numbers.
[]float64{1e20, 3, 1, 4, 1, 5, 9, -1e20},
[]float64{10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 0, 0, .11},
[]float64{10, 20, 30, 40, 50, -100, 4.7, -11e2},
} {
fmt.Println("Vector:", v)
if m, ok := mean(v); ok {
fmt.Printf("Mean of %d numbers is %g\n\n", len(v), m)
} else {
fmt.Println("Mean undefined\n")
}
}
}</lang>
- Output:
Vector: [] Mean undefined Vector: [+Inf +Inf] Mean of 2 numbers is +Inf Vector: [+Inf -Inf] Mean of 2 numbers is NaN Vector: [3 1 4 1 5 9] Mean of 6 numbers is 3.8333333333333335 Vector: [1e+20 3 1 4 1 5 9 -1e+20] Mean of 8 numbers is 2.875 Vector: [10 9 8 7 6 5 4 3 2 1 0 0 0 0 0.11] Mean of 15 numbers is 3.674 Vector: [10 20 30 40 50 -100 4.7 -1100] Mean of 8 numbers is -130.6625
Groovy
<lang groovy>def avg = { list -> list == [] ? 0 : list.sum() / list.size() }</lang>
Test Program: <lang groovy>println avg(0..9) println avg([2,2,2,4,2]) println avg ([])</lang>
Output:
4.5 2.4 0
Haskell
This function works if the element type is an instance of Fractional: <lang haskell>mean :: (Fractional a) => [a] -> a mean [] = 0 mean xs = sum xs / Data.List.genericLength xs</lang>
But some types, e.g. integers, are not Fractional; the following function works for all Real types: <lang haskell>meanReals :: (Real a, Fractional b) => [a] -> b meanReals = mean . map realToFrac</lang>
If you want to avoid keeping the list in memory and traversing it twice:
<lang haskell>{-# LANGUAGE BangPatterns #-} import Data.List (foldl') mean :: (Real n, Fractional m) => [n] -> m mean xs = let (s,l) = foldl' f (0, 0) xs in realToFrac s / l
where f (!s,!l) x = (s+x,l+1)</lang>
HicEst
<lang hicest>REAL :: vec(100) ! no zero-length arrays in HicEst
vec = $ - 1/2 ! 0.5 ... 99.5 mean = SUM(vec) / LEN(vec) ! 50
END </lang>
Icon and Unicon
<lang icon>procedure main(args)
every (s := 0) +:= !args write((real(s)/(0 ~= *args)) | 0)
end</lang>
Sample outputs:
->am 1 2 3 4 5 6 7 4.0 ->am 0 ->
IDL
If truly only the mean is wanted, one could use
<lang idl>x = [3,1,4,1,5,9] print,mean(x)</lang>
But mean() is just a thin wrapper returning the zeroth element of moment() :
<lang idl>print,moment(x)
- ==>
3.83333 8.96667 0.580037 -1.25081</lang>
which are mean, variance, skewness and kurtosis.
There are no zero-length vectors in IDL. Every variable has at least one value or otherwise it is <Undefined>.
J
<lang j>mean=: +/ % #</lang>
That is, sum divided by the number of items. The verb also works on higher-ranked arrays. For example:
<lang j> mean 3 1 4 1 5 9 3.83333
mean $0 NB. $0 is a zero-length vector
0
x=: 20 4 ?@$ 0 NB. a 20-by-4 table of random (0,1) numbers mean x
0.58243 0.402948 0.477066 0.511155</lang>
The computation can also be written as a loop. It is shown here for comparison only and is highly non-preferred compared to the version above.
<lang j>mean1=: 3 : 0
z=. 0
for_i. i.#y do. z=. z+i{y end.
z % #y
)
mean1 3 1 4 1 5 9
3.83333
mean1 $0
0
mean1 x
0.58243 0.402948 0.477066 0.511155</lang>
Java
Assume the numbers are in a double array called "nums". <lang java5>... double sum = 0; for(double i : nums){
sum += i;
} System.out.println("The mean is: " + ((nums.length != 0) ? (sum / nums.length) : 0)); ...</lang>
JavaScript
<lang javascript>function mean(array) {
var sum = 0, i;
for (i = 0; i < array.length; i++)
{
sum += array[i];
}
return array.length ? sum / array.length : 0;
}
alert( mean( [1,2,3,4,5] ) ); // 3</lang>
<lang javascript>function mean(a) {
return a.length ? Functional.reduce('+', 0, a) / a.length : 0;
}</lang>
Julia
Julia's built-in mean function accepts AbstractArrays (vector, matrix, etc.) <lang julia>julia> mean([1,2,3]) 2.0 julia> mean(1:10) 5.5 julia> mean([]) ERROR: mean of empty collection undefined: []</lang>
K
<lang k> mean: {(+/x)%#x}
mean 1 2 3 5 7
3.6
mean@!0 / empty array
0.0</lang>
LabVIEW
This image is a VI Snippet, an executable image of LabVIEW code. The LabVIEW version is shown on the top-right hand corner. You can download it, then drag-and-drop it onto the LabVIEW block diagram from a file browser, and it will appear as runnable, editable code.
Logo
<lang logo>to average :l
if empty? :l [output 0] output quotient apply "sum :l count :l
end print average [1 2 3 4] ; 2.5</lang>
Liberty BASIC
<lang lb>total=17 dim nums(total) for i = 1 to total
nums(i)=i-1
next
for j = 1 to total
sum=sum+nums(j)
next if total=0 then mean=0 else mean=sum/total print "Arithmetic mean: ";mean
</lang>
LSL
<lang LSL>integer MAX_ELEMENTS = 10; integer MAX_VALUE = 100; default {
state_entry() {
list lst = [];
integer x = 0;
for(x=0 ; x<MAX_ELEMENTS ; x++) {
lst += llFrand(MAX_VALUE);
}
llOwnerSay("lst=["+llList2CSV(lst)+"]");
llOwnerSay("Geometric Mean: "+(string)llListStatistics(LIST_STAT_GEOMETRIC_MEAN, lst));
llOwnerSay(" Max: "+(string)llListStatistics(LIST_STAT_MAX, lst));
llOwnerSay(" Mean: "+(string)llListStatistics(LIST_STAT_MEAN, lst));
llOwnerSay(" Median: "+(string)llListStatistics(LIST_STAT_MEDIAN, lst));
llOwnerSay(" Min: "+(string)llListStatistics(LIST_STAT_MIN, lst));
llOwnerSay(" Num Count: "+(string)llListStatistics(LIST_STAT_NUM_COUNT, lst));
llOwnerSay(" Range: "+(string)llListStatistics(LIST_STAT_RANGE, lst));
llOwnerSay(" Std Dev: "+(string)llListStatistics(LIST_STAT_STD_DEV, lst));
llOwnerSay(" Sum: "+(string)llListStatistics(LIST_STAT_SUM, lst));
llOwnerSay(" Sum Squares: "+(string)llListStatistics(LIST_STAT_SUM_SQUARES, lst));
}
}</lang> Output:
lst=[23.815209, 85.890704, 10.811144, 31.522696, 54.619416, 12.211729, 42.964463, 87.367889, 7.106129, 18.711078]
Geometric Mean: 27.325070
Max: 87.367889
Mean: 37.502046
Median: 27.668953
Min: 7.106129
Num Count: 10.000000
Range: 80.261761
Std Dev: 29.819840
Sum: 375.020458
Sum Squares: 22067.040048
Lua
<lang lua>function mean (numlist)
if type(numlist) ~= 'table' then return numlist end num = 0 table.foreach(numlist,function(i,v) num=num+v end) return num / #numlist
end
print (mean({3,1,4,1,5,9}))</lang>
Lucid
<lang lucid>avg(x)
where sum = first(x) fby sum + next(x); n = 1 fby n + 1; avg = sum / n; end</lang>
M4
M4 handle only integers, so in order to have a slightly better math for the mean, we must pass to the mean macro integers multiplied by 100. The macro rmean could embed the macro fmean and extractdec directly, but it is a little bit clearer to keep them separated.
<lang m4>define(`extractdec', `ifelse(eval(`$1%100 < 10'),1,`0',`')eval($1%100)')dnl define(`fmean', `eval(`($2/$1)/100').extractdec(eval(`$2/$1'))')dnl define(`mean', `rmean(`$#', $@)')dnl define(`rmean', `ifelse(`$3', `', `fmean($1,$2)',dnl `rmean($1, eval($2+$3), shift(shift(shift($@))))')')dnl</lang> <lang m4>mean(0,100,200,300,400,500,600,700,800,900,1000)</lang>
Maple
This version accepts any indexable structure, including numeric arrays. We use a call to the "environment variable" (dynamically scoped global) "Normalizer" to provide normalization of symbolic expressions. This can be set by the caller to adjust the strength of normalization desired. <lang Maple> mean := proc( a :: indexable )
local i;
Normalizer( add( i, i in a ) / numelems( a ) )
end proc: </lang> For example: <lang Maple> > mean( { 1/2, 2/3, 3/4, 4/5, 5/6 } ); # set
71
---
100
> mean( [ a, 2, c, 2.3, e ] ); # list
0.8600000000 + a/5 + c/5 + e/5
> mean( Array( [ 1, sin( s ), 3, exp( I*t ), 5 ] ) ); # array
9/5 + 1/5 sin(s) + 1/5 exp(t I)
> mean( [ sin(s)^2, cos(s)^2 ] );
2 2
1/2 sin(s) + 1/2 cos(s)
> Normalizer := simplify: # use a stronger normalizer than the default > mean( [ sin(s)^2, cos(s)^2 ] );
1/2
> mean([]); # empty argument causes an exception to be raised. Error, (in mean) numeric exception: division by zero </lang> A slightly different design computes the mean of all its arguments, instead of requiring a single container argument. This seems a little more Maple-like for a general purpose utility. <lang Maple>mean := () -> Normalizer( `+`( args ) / nargs ):</lang> This can be called as in the following examples. <lang Maple> > mean( 1, 2, 3, 4, 5 );
3
> mean( a + b, b + c, c + d, d + e, e + a );
2 a 2 b 2 c 2 d 2 e
--- + --- + --- + --- + ---
5 5 5 5 5
> mean(); # again, an exception is raised Error, (in mean) numeric exception: division by zero </lang> If desired, we can add argument type-checking as follows. <lang Maple>mean := ( s :: seq(algebraic) ) -> Normalizer( `+`( args ) / nargs ):</lang>
Mathematica
Modify the built-in Mean function to give 0 for empty vectors (lists in Mathematica): <lang mathematica>Unprotect[Mean]; Mean[{}] := 0</lang> Examples: <lang mathematica>Mean[{3,4,5}] Mean[{3.2,4.5,5.9}] Mean[{-4, 1.233}] Mean[{}] Mean[{1/2,1/3,1/4,1/5}] Mean[{a,c,Pi,-3,a}]</lang> gives (a set of integers gives back an integer or a rational, a set of floats gives back a float, a set of rationals gives a rational back, a list of symbols and numbers keeps the symbols exact and a mix of exact and approximate numbers gives back an approximate number): <lang mathematica>4 4.53333 -1.3835 0 77/240 1/5 (-3+2 a+c+Pi)</lang>
Mathprog
Summing the vector and then dividing the sum by the vector's length is slightly less boring than calling a builtin function Mean or similar.
Mathprog is never boring so this program finds a number M such that when M is subtracted from each value in the vector a second vector is formed with the property that the sum of the elements in the second vector is zero. In this case M is the Arithmetic Mean.
Euclid proved that for any vector there is only one such number and from this derived the Division Theorem.
To make it more interesting I find the Arithmectic Mean of more than a million Integers.
<lang> /*Arithmetic Mean of a large number of Integers
- or - solve a very large constraint matrix
over 1 million rows and columns
Nigel_Galloway
March 18th., 2008.
- /
param e := 20; set Sample := {1..2**e-1};
var Mean; var E{z in Sample};
/* sum of variances is zero */ zumVariance: sum{z in Sample} E[z] = 0;
/* Mean + variance[n] = Sample[n] */ variances{z in Sample}: Mean + E[z] = z;
solve;
printf "The arithmetic mean of the integers from 1 to %d is %f\n", 2**e-1, Mean;
end; </lang>
When run this produces:
<lang> GLPSOL: GLPK LP/MIP Solver, v4.47 Parameter(s) specified in the command line:
--nopresol --math AM.mprog
Reading model section from AM.mprog... 24 lines were read Generating zumVariance... Generating variances... Model has been successfully generated Scaling...
A: min|aij| = 1.000e+000 max|aij| = 1.000e+000 ratio = 1.000e+000
Problem data seem to be well scaled Constructing initial basis... Size of triangular part = 1048575 GLPK Simplex Optimizer, v4.47 1048576 rows, 1048576 columns, 3145725 non-zeros
0: obj = 0.000000000e+000 infeas = 5.498e+011 (1)
- 1: obj = 0.000000000e+000 infeas = 0.000e+000 (0)
OPTIMAL SOLUTION FOUND Time used: 2.0 secs Memory used: 1393.8 Mb (1461484590 bytes) The arithmetic mean of the integers from 1 to 1048575 is 524288.000000 Model has been successfully processed </lang>
MATLAB
<lang Matlab>function meanValue = findmean(setOfValues)
meanValue = mean(setOfValues);
end</lang>
Maxima
<lang maxima>mean([2, 7, 11, 17]);</lang>
MAXScript
<lang maxscript>fn mean data = (
total = 0
for i in data do
(
total += i
)
if data.count == 0 then 0 else total as float/data.count
)
print (mean #(3, 1, 4, 1, 5, 9))</lang>
МК-61/52
<lang>0 П0 П1 С/П ИП0 ИП1 * + ИП1 1 + П1 / П0 БП 03</lang>
Instruction: В/О С/П Number С/П Number ...
Each time you press the С/П on the indicator would mean already entered numbers.
Modula-2
<lang modula2>PROCEDURE Avg;
VAR avg : REAL;
BEGIN
avg := sx / n;
InOut.WriteString ("Average = ");
InOut.WriteReal (avg, 8, 2);
InOut.WriteLn
END Avg;</lang> OR <lang modula2>PROCEDURE Average (Data : ARRAY OF REAL; Samples : CARDINAL) : REAL;
(* Calculate the average over 'Samples' values, stored in array 'Data'. *)
VAR sum : REAL;
n : CARDINAL;
BEGIN
sum := 0.0; FOR n := 0 TO Samples - 1 DO sum := sum + Data [n] END; RETURN sum / FLOAT(Samples)
END Average;</lang>
MUMPS
<lang MUMPS>MEAN(X)
;X is assumed to be a list of numbers separated by "^" QUIT:'$DATA(X) "No data" QUIT:X="" "Empty Set" NEW S,I SET S=0,I=1 FOR QUIT:I>$L(X,"^") SET S=S+$P(X,"^",I),I=I+1 QUIT (S/$L(X,"^"))</lang>
USER>W $$MEAN^ROSETTA
No data
USER>W $$MEAN^ROSETTA("")
Empty Set
USER>
USER>W $$MEAN^ROSETTA("1^6^12^4")
5.75
Nemerle
<lang Nemerle>using System; using System.Console; using Nemerle.Collections;
module Mean {
ArithmeticMean(x : list[int]) : double
{
|[] => 0.0
|_ =>(x.FoldLeft(0, _+_) :> double) / x.Length
}
Main() : void
{
WriteLine("Mean of [1 .. 10]: {0}", ArithmeticMean($[1 .. 10]));
}
}</lang>
NetRexx
<lang NetRexx>/* NetRexx */ options replace format comments java crossref symbols nobinary
launchSample() return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ method arithmeticMean(vv = Vector) public static signals DivideException returns Rexx
sum = 0 n_ = Rexx loop n_ over vv sum = sum + n_ end n_ mean = sum / vv.size()
return mean
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ method launchSample() public static
TRUE_ = 1 == 1
FALSE_ = \TRUE_
tracing = FALSE_
vectors = getSampleData()
loop v_ = 0 to vectors.length - 1
say 'Average of:' vectors[v_].toString()
do
say ' =' arithmeticMean(vectors[v_])
catch dex = DivideException
say 'Caught "Divide By Zero"; bypassing...'
if tracing then dex.printStackTrace()
catch xex = RuntimeException
say 'Caught unspecified run-time exception; bypassing...'
if tracing then xex.printStackTrace()
end
say
end v_
return
-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ method getSampleData() private static returns Vector[]
seed = 1066 rng = Random(seed) vectors =[ - Vector(Arrays.asList([Rexx 1, 2, 3, 4, 5, 6, 7, 8, 9, 10])), - Vector(), - Vector(Arrays.asList([Rexx rng.nextInt(seed), rng.nextInt(seed), rng.nextInt(seed), rng.nextInt(seed), rng.nextInt(seed), rng.nextInt(seed)])), - Vector(Arrays.asList([Rexx rng.nextDouble(), rng.nextDouble(), rng.nextDouble(), rng.nextDouble(), rng.nextDouble(), rng.nextDouble(), rng.nextDouble()])), - Vector(Arrays.asList([Rexx '1.0', '2.0', 3.0])), - Vector(Arrays.asList([Rexx '1.0', 'not a number', 3.0])) - ] return vectors
</lang> Output:
Average of: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
= 5.5
Average of: []
Caught "Divide By Zero"; bypassing...
Average of: [294, 726, 945, 828, 1031, 825]
= 774.833333
Average of: [0.3318379308729921, 0.7612271993941618, 0.9517290891755477, 0.7687823629521795, 0.2201768257213939, 0.1083471020993242, 0.5158554699332363]
= 0.52256514
Average of: [1.0, 2.0, 3.0]
= 2
Average of: [1.0, not a number, 3.0]
Caught unspecified run-time exception; bypassing...
NewLISP
<lang NewLISP>(define (Mean Lst)
(if (empty? Lst)
0
(/ (apply + Lst) (length Lst))))
(Mean (sequence 1 1000))-> 500
(Mean '()) -> 0</lang>
Nial
in the standard way, mean is <lang nial>mean is / [sum, tally]
mean 6 2 4 = 4</lang> but it fails with 0 length vectors. so using a tally with a minimum value 1
<lang nial>dtally is recur [ empty rest, 1 first, 1 first, plus, rest ] mean is / [sum, dtally]
mean [] =0</lang>
Niue
<lang Niue> [ [ , len 1 - at ! ] len 3 - times swap , ] 'map ; ( a Lisp like map, to sum the stack ) [ len 'n ; [ + ] 0 n swap-at map n / ] 'avg ;
1 2 3 4 5 avg . => 3 3.4 2.3 .01 2.0 2.1 avg . => 1.9619999999999997 </lang>
Oberon-2
Oxford Oberon-2 <lang oberon2> MODULE AvgMean; IMPORT Out; CONST MAXSIZE = 10; PROCEDURE Avg(a: ARRAY OF REAL; items: INTEGER): REAL; VAR i: INTEGER; total: REAL; BEGIN total := 0.0; FOR i := 0 TO LEN(a) - 1 DO total := total + a[i] END; RETURN total/LEN(a) END Avg; VAR ary: ARRAY MAXSIZE OF REAL; BEGIN ary[0] := 10.0; ary[1] := 11.01; ary[2] := 12.02; ary[3] := 13.03; ary[4] := 14.04; ary[5] := 15.05; ary[6] := 16.06; ary[7] := 17.07; ary[8] := 18.08; ary[9] := 19.09; Out.Fixed(Avg(ary),4,2);Out.Ln END AvgMean. </lang> Output:
14.55
Objeck
<lang objeck> function : native : PrintAverage(values : FloatVector) ~ Nil {
values->Average()->PrintLine();
} </lang>
OCaml
These functions return a float:
<lang ocaml>let mean_floats = function
| [] -> 0. | xs -> List.fold_left (+.) 0. xs /. float_of_int (List.length xs)
let mean_ints xs = mean_floats (List.map float_of_int xs)</lang>
the previous code is easier to read and understand, though if you wish the fastest implementation to use in production code notice several points: it is possible to save a call to List.length computing the length through the List.fold_left, and for mean_ints it is possible to save calling float_of_int on every numbers, converting only the result of the addition. (also when using List.map and when the order is not important, you can use List.rev_map instead to save an internal call to List.rev). Also the task asks to return 0 on empty lists, but in OCaml this case would rather be handled by an exception.
<lang ocaml>let mean_floats xs =
if xs = [] then
invalid_arg "empty list"
else
let total, length =
List.fold_left
(fun (tot,len) x -> (x +. tot), len +. 1.)
(0., 0.) xs
in
(total /. length)
let mean_ints xs =
if xs = [] then
invalid_arg "empty list"
else
let total, length =
List.fold_left
(fun (tot,len) x -> (x + tot), len +. 1.)
(0, 0.) xs
in
(float total /. length)
- </lang>
Octave
GNU Octave has a mean function (from statistics package), but it does not handle an empty vector; an implementation that allows that is:
<lang octave>function m = omean(l)
if ( numel(l) == 0 ) m = 0; else m = mean(l); endif
endfunction
disp(omean([])); disp(omean([1,2,3]));</lang>
If the data contains missing value, encoded as non-a-number:
<lang octave>function m = omean(l)
n = sum(~isnan(l));
l(isnan(l))=0;
s = sum(l);
m = s./n;
end;</lang>
ooRexx
<lang ooRexx> call testAverage .array~of(10, 9, 8, 7, 6, 5, 4, 3, 2, 1) call testAverage .array~of(10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 0, 0, .11) call testAverage .array~of(10, 20, 30, 40, 50, -100, 4.7, -11e2) call testAverage .array~new
- routine testAverage
use arg numbers
say "numbers =" numbers~toString("l", ", ")
say "average =" average(numbers)
say
- routine average
use arg numbers -- return zero for an empty list if numbers~isempty then return 0
sum = 0
do number over numbers
sum += number
end
return sum/numbers~items
</lang> Output:
numbers = 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 average = 5.5 numbers = 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 0, 0, .11 average = 3.674 numbers = 10, 20, 30, 40, 50, -100, 4.7, -1100 average = -130.6625 numbers = average = 0
Oz
A version working on floats: <lang oz>declare
fun {Mean Xs}
{FoldL Xs Number.'+' 0.0} / {Int.toFloat {Length Xs}}
end
in
{Show {Mean [3. 1. 4. 1. 5. 9.]}}</lang>
PARI/GP
<lang parigp>avg(v)={
if(#v,vecsum(v)/#v)
};</lang>
Pascal
<lang pascal>Program Mean;
function DoMean(vector: array of double): double;
var
sum: double;
i, len: integer;
begin
sum := 0;
len := length(vector);
if len > 0 then
begin
for i := low(vector) to high(vector) do
sum := sum + vector[i];
sum := sum / len;
end;
DoMean := sum;
end;
const
vector: array [3..8] of double = (3.0, 1.0, 4.0, 1.0, 5.0, 9.0);
var
i: integer;
begin
writeln('Calculating the arithmetic mean of a series of numbers:');
write('Numbers: [ ');
for i := low(vector) to high(vector) do
write (vector[i]:3:1, ' ');
writeln (']');
writeln('Mean: ', DoMean(vector):10:8);
end.</lang>
Output:
Calculating the arithmetic mean of a series of numbers: Numbers: [ 3.0 1.0 4.0 1.0 5.0 9.0 ] Mean: 3.83333333
Alternative version using the Math unit:
<lang pascal>Program DoMean; uses math; const
vector: array [3..8] of double = (3.0, 1.0, 4.0, 1.0, 5.0, 9.0);
var
i: integer; mean: double;
begin
writeln('Calculating the arithmetic mean of a series of numbers:');
write('Numbers: [ ');
for i := low(vector) to high(vector) do
write (vector[i]:3:1, ' ');
writeln (']');
mean := 0;
if length(vector) > 0 then
mean := sum(vector)/length(vector);
writeln('Mean: ', mean:10:8);
end.</lang>
Perl
<lang perl>sub avg {
@_ or return 0; my $sum = 0; $sum += $_ foreach @_; return $sum/@_;
}
print avg(qw(3 1 4 1 5 9)), "\n";</lang>
With module Data::Average. (For zero-length arrays, returns the empty list.) <lang perl>use Data::Average;
my $d = Data::Average->new; $d->add($_) foreach qw(3 1 4 1 5 9); print $d->avg, "\n";</lang>
Perl 6
<lang perl6>sub mean (@a) { ([+] @a) / (@a || 1) }</lang>
PHP
<lang php>$nums = array(3, 1, 4, 1, 5, 9); if ($nums)
echo array_sum($nums) / count($nums), "\n";
else
echo "0\n";</lang>
PL/I
<lang PL/I> arithmetic_mean = sum(A)/dimension(A,1); </lang>
PicoLisp
<lang PicoLisp>(de mean (Lst)
(if (atom Lst)
0
(/ (apply + Lst) (length Lst)) ) )</lang>
Output:
: (mean (range 1 1000)) -> 500
Pop11
<lang pop11>define mean(v);
lvars n = length(v), i, s = 0;
if n = 0 then
return(0);
else
for i from 1 to n do
s + v(i) -> s;
endfor;
endif;
return(s/n);
enddefine;</lang>
PostScript
<lang> /findmean{ /x exch def /sum 0 def /i 0 def x length 0 eq {} { x length{ /sum sum x i get add def /i i 1 add def }repeat /sum sum x length div def }ifelse sum == }def </lang>
<lang postscript> /avg {
dup length
{0 gt} {
exch 0 {add} fold exch div
} {
exch pop
} ifte
}. </lang>
PowerShell
The hard way by calculating a sum and dividing: <lang powershell>function mean ($x) {
if ($x.Count -eq 0) {
return 0
} else {
$sum = 0
foreach ($i in $x) {
$sum += $i
}
return $sum / $x.Count
}
}</lang>
or, shorter, by using the Measure-Object cmdlet which already knows how to compute an average:
<lang powershell>function mean ($x) {
if ($x.Count -eq 0) {
return 0
} else {
return ($x | Measure-Object -Average).Average
}
}</lang>
PureBasic
<lang PureBasic>Procedure.d mean(List number())
Protected sum=0
ForEach number() sum + number() Next ProcedureReturn sum / ListSize(number()) ; Depends on programm if zero check needed, returns nan on division by zero
EndProcedure</lang>
Python
.
Uses fsum which tracks multiple partial sums to avoid losing precision <lang python>from math import fsum def average(x):
return fsum(x)/float(len(x)) if x else 0
print (average([0,0,3,1,4,1,5,9,0,0])) print (average([1e20,-1e-20,3,1,4,1,5,9,-1e20,1e-20]))</lang>
- Output:
<lang python>2.3 2.3</lang>
<lang python>def average(x):
return sum(x)/float(len(x)) if x else 0
print (average([0,0,3,1,4,1,5,9,0,0])) print (average([1e20,-1e-20,3,1,4,1,5,9,-1e20,1e-20]))</lang>
- Output:
(Notice how the second call gave the wrong result) <lang python>2.3 1e-21</lang>
<lang python>def avg(data):
if len(data)==0:
return 0
else:
return sum(data)/float(len(data))
print avg([0,0,3,1,4,1,5,9,0,0])</lang>
- Output:
<lang python>2.3</lang>
R
R has its mean function but it does not allow for NULL (void vectors or whatever) as argument: in this case it raises a warning and the result is NA. An implementation that does not suppress the warning could be:
<lang R>omean <- function(v) {
m <- mean(v) ifelse(is.na(m), 0, m)
}</lang>
Racket
Racket's math library (available in v5.3.2 and newer) comes with a mean function that works on arbitrary sequences.
<lang racket>
- lang racket
(require math)
(mean (in-range 0 1000)) ; -> 499 1/2 (mean '(2 2 4 4)) ; -> 3 (mean #(3 4 5 8)) ; -> 5 </lang>
REBOL
<lang REBOL>rebol [
Title: "Arithmetic Mean (Average)" Author: oofoe Date: 2009-12-11 URL: http://rosettacode.org/wiki/Average/Arithmetic_mean
]
average: func [v /local sum][ if empty? v [return 0]
sum: 0 forall v [sum: sum + v/1] sum / length? v ]
- Note precision loss as spread increased.
print [mold x: [] "->" average x] print [mold x: [3 1 4 1 5 9] "->" average x] print [mold x: [1000 3 1 4 1 5 9 -1000] "->" average x] print [mold x: [1e20 3 1 4 1 5 9 -1e20] "->" average x]</lang>
Output:
[] -> 0 [3 1 4 1 5 9] -> 3.83333333333333 [1000 3 1 4 1 5 9 -1000] -> 2.875 [1E+20 3 1 4 1 5 9 -1E+20] -> 0.0
REXX
The vectors (list) can contain any valid numbers. <lang rexx>/*REXX pgm finds the averages/arithmetic mean of several lists (vectors)*/ @.1 = 10 9 8 7 6 5 4 3 2 1 @.2 = 10 9 8 7 6 5 4 3 2 1 0 0 0 0 .11 @.3 = '10 20 30 40 50 -100 4.7 -11e2' @.4 = '1 2 3 4 five 6 7 8 9 10.1. ±2' @.5 = 'World War I & World War II' @.6 =
do j=1 for 6
say 'numbers = ' @.j; say 'average = ' avg(@.j); say
end /*t*/
exit /*stick a fork in it, we're done.*/ /*──────────────────────────────────AVG subroutine──────────────────────*/ avg: procedure; parse arg x; w=words(x); s=0; $=left(,20) if w==0 then return 'N/A: ───[null vector.]'
do k=1 for w; _=word(x,k)
if datatype(_,'N') then do; s=s+_; iterate; end
say $ '***error!*** non-numeric: ' _; w=w-1 /*adjust W*/
end /*k*/
if w==0 then return 'N/A: ───[no numeric values.]' return s/max(1,w)</lang> output
numbers = 10 9 8 7 6 5 4 3 2 1
average = 5.5
numbers = 10 9 8 7 6 5 4 3 2 1 0 0 0 0 .11
average = 3.674
numbers = 10 20 30 40 50 -100 4.7 -11e2
average = -130.6625
numbers = 1 2 3 4 five 6 7 8 9 10.1. ±2
***error!*** non-numeric: five
***error!*** non-numeric: 10.1.
***error!*** non-numeric: ±2
average = 5
numbers = World War I & World War II
***error!*** non-numeric: World
***error!*** non-numeric: War
***error!*** non-numeric: I
***error!*** non-numeric: &
***error!*** non-numeric: World
***error!*** non-numeric: War
***error!*** non-numeric: II
average = N/A: ───[no numeric values.]
numbers =
average = N/A: ───[null vector.]
Ruby
<lang ruby>nums = [3, 1, 4, 1, 5, 9] nums.empty? ? 0 : nums.inject(:+) / Float(nums.size)</lang>
Run BASIC
<lang runbasic>print "Gimme the number in the array:";input numArray dim value(numArray) for i = 1 to numArray
value(i) = i * 1.5
next
for i = 1 to total
totValue = totValue +value(numArray)
next if totValue <> 0 then mean = totValue/numArray print "The mean is: ";mean</lang>
Sather
Built to work with VEC, ("geometric" vectors), whose elements must be floats. A 0-dimension vector yields "nan". <lang sather>class VECOPS is
mean(v:VEC):FLT is m ::= 0.0; loop m := m + v.aelt!; end; return m / v.dim.flt; end;
end;
class MAIN is
main is v ::= #VEC(|1.0, 5.0, 7.0|); #OUT + VECOPS::mean(v) + "\n"; end;
end;</lang>
Scala
Using Scala 2.7, this has to be defined for each numeric type:
<lang scala>def mean(s: Seq[Int]) = s.foldLeft(0)(_+_) / s.size</lang>
However, Scala 2.8 gives much more flexibility, but you still have to opt between integral types and fractional types. For example:
<lang scala>def mean[T](s: Seq[T])(implicit n: Integral[T]) = {
import n._ s.foldLeft(zero)(_+_) / fromInt(s.size)
}</lang>
This can be used with any subclass of Sequence on integral types, up to and including BigInt. One can also create singletons extending Integral for user-defined numeric classes. Likewise, Integral can be replaced by Fractional in the code to support fractional types, such as Float and Double.
Alas, Scala 2.8 also simplifies the task in another way:
<lang scala>def mean[T](s: Seq[T])(implicit n: Fractional[T]) = n.div(s.sum, n.fromInt(s.size))</lang>
Here we show a function that supports fractional types. Instead of importing the definitions from n, we are calling them on n itself. And because we did not import them, the implicit definitions that would allow us to use / were not imported as well. Finally, we use sum instead of foldLeft.
Scheme
<lang scheme>(define (mean l)
(if (null? l)
0
(/ (apply + l) (length l))))</lang>
> (mean (list 3 1 4 1 5 9)) 3 5/6
Seed7
<lang seed7>$ include "seed7_05.s7i";
include "float.s7i";
const array float: numVector is [] (1.0, 2.0, 3.0, 4.0, 5.0);
const func float: mean (in array float: numbers) is func
result
var float: result is 0.0;
local
var float: total is 0.0;
var float: num is 0.0;
begin
if length(numbers) <> 0 then
for num range numbers do
total +:= num;
end for;
result := total / flt(length(numbers));
end if;
end func;
const proc: main is func
begin writeln(mean(numVector)); end func;</lang>
Slate
<lang slate>[|:list| (list reduce: #+ `er ifEmpty: [0]) / (list isEmpty ifTrue: [1] ifFalse: [list size])] applyWith: #(3 1 4 1 5 9). [|:list| (list reduce: #+ `er ifEmpty: [0]) / (list isEmpty ifTrue: [1] ifFalse: [list size])] applyWith: {}.</lang>
Smalltalk
<lang smalltalk> | numbers |
numbers := #(1 2 3 4 5 6 7 8). (numbers isEmpty
ifTrue:[0]
ifFalse: [
(numbers inject: 0 into: [:sumSoFar :eachElement | sumSoFar + eachElement]) / numbers size ]
) displayNl. </lang> However, the empty check can be omitted, as inject returns the injected value for empty collections, and we probably do not care for the average of nothing (i.e. the division by zero exception): <lang smalltalk> | numbers |
numbers := #(1 2 3 4 5 6 7 8). ( numbers inject: 0 into: [:sumSoFar :eachElement | sumSoFar + eachElement]) / numbers size] ) displayNl. </lang> also, most Smalltalk's collection classes already provide sum and average methods, which makes it:
<lang smalltalk> | numbers |
numbers := #(1 2 3 4 5 6 7 8). (numbers sum / numbers size) displayNl. </lang> or <lang smalltalk> | numbers |
numbers := #(1 2 3 4 5 6 7 8). numbers average displayNl. </lang>
SNOBOL4
<lang SNOBOL4> define('avg(a)i,sum') :(avg_end) avg i = i + 1; sum = sum + a :s(avg)
avg = 1.0 * sum / prototype(a) :(return)
avg_end
- # Fill arrays
str = '1 2 3 4 5 6 7 8 9 10'; arr = array(10)
loop i = i + 1; str len(p) span('0123456789') . arr @p :s(loop)
empty = array(1) ;* Null vector
- # Test and display
output = '[' str '] -> ' avg(arr)
output = '[ ] -> ' avg(empty)
end</lang>
Output:
[1 2 3 4 5 6 7 8 9 10] -> 5.5 [ ] -> 0.
Standard ML
These functions return a real:
<lang sml>fun mean_reals [] = 0.0
| mean_reals xs = foldl op+ 0.0 xs / real (length xs);
val mean_ints = mean_reals o (map real);</lang>
The previous code is easier to read and understand, though if you want
the fastest implementation to use in production code notice several points:
it is possible to save a call to length computing the length through
the foldl, and for mean_ints it is possible to save calling
real on every numbers, converting only the result of the addition.
Also the task asks to return 0 on empty lists, but in Standard ML this case
would rather be handled by an exception.
<lang sml>fun mean_reals [] = raise Empty
| mean_reals xs = let
val (total, length) =
foldl
(fn (x, (tot,len)) => (x + tot, len + 1.0))
(0.0, 0.0) xs
in
(total / length)
end;
fun mean_ints [] = raise Empty
| mean_ints xs = let
val (total, length) =
foldl
(fn (x, (tot,len)) => (x + tot, len + 1.0))
(0, 0.0) xs
in
(real total / length)
end;</lang>
Tcl
<lang tcl>package require Tcl 8.5 proc mean args {
if {[set num [llength $args]] == 0} {return 0}
expr {[tcl::mathop::+ {*}$args] / double($num)}
} mean 3 1 4 1 5 9 ;# ==> 3.8333333333333335</lang>
TI-89 BASIC
<lang ti89b>Define rcmean(nums) = when(dim(nums) = 0, 0, mean(nums))</lang>
Trith
<lang trith>: mean dup empty? [drop 0] [dup [+] foldl1 swap length /] branch ;
[3 1 4 1 5 9] mean</lang>
UnixPipes
Uses ksh93-style process substitution. Also overwrites the file named count in the current directory.
<lang bash>term() {
b=$1;res=$2 echo "scale=5;$res+$b" | bc
}
sum() {
(read B; res=$1; test -n "$B" && (term $B $res) || (term 0 $res))
}
fold() {
func=$1
(while read a ; do
fold $func | $func $a
done)
}
mean() {
tee >(wc -l > count) | fold sum | xargs echo "scale=5;(1/" $(cat count) ") * " | bc
}
(echo 3; echo 1; echo 4) | mean</lang>
UNIX Shell
This example uses expr, so it only works with integers. It checks that each string in the list is an integer.
<lang bash>mean() { if expr $# >/dev/null; then (count=0 sum=0 while expr $# \> 0 >/dev/null; do sum=`expr $sum + "$1"` result=$? expr $result \> 1 >/dev/null && exit $result
count=`expr $count + 1` shift done expr $sum / $count) else echo 0 fi }
printf "test 1: "; mean # 0 printf "test 2: "; mean 300 # 300 printf "test 3: "; mean 300 100 400 # 266 printf "test 4: "; mean -400 400 -1300 200 # -275 printf "test 5: "; mean - # expr: syntax error printf "test 6: "; mean 1 2 A 3 # expr: non-numeric argument</lang>
Ursala
There is a library function for means already, although it doesn't cope with empty vectors. A mean function could be defined as shown for this task. <lang Ursala>#import nat
- import flo
mean = ~&?\0.! div^/plus:-0. float+ length
- cast %e
example = mean <5.,3.,-2.,6.,-4.></lang> output:
1.600000e+00
V
<lang v>[mean
[sum 0 [+] fold]. dup sum swap size [[1 <] [1]] when /
].</lang>
Vala
Using array to hold the numbers of the list: <lang vala> double arithmetic(double[] list){ double mean; double sum = 0;
if (list.length == 0) return 0.0; foreach(double number in list){ sum += number; } // foreach
mean = sum / list.length;
return mean; } // end arithmetic mean
public static void main(){ double[] test = {1.0, 2.0, 5.0, -5.0, 9.5, 3.14159}; double[] zero_len = {};
double mean = arithmetic(test); double mean_zero = arithmetic(zero_len);
stdout.printf("%s\n", mean.to_string()); stdout.printf("%s\n", mean_zero.to_string()); } </lang>
Output:
2.6069316666666666 0
Vedit macro language
The numeric data is stored in current edit buffer as ASCII strings, one value per line. <lang vedit>#1 = 0 // Sum
- 2 = 0 // Count
BOF While(!At_EOF) {
#1 += Num_Eval(SIMPLE) #2++ Line(1, ERRBREAK)
} if (#2) { #1 /= #2 } Num_Type(#1)</lang>
XPL0
<lang XPL0>code CrLf=9; code real RlOut=48;
func real Mean(A, N); real A; int N; real S; int I; [if N=0 then return 0.0; S:= 0.0; for I:= 0 to N-1 do
S:= S+A(I);
return S/float(N); ]; \Mean
real Test; [Test:= [1.0, 2.0, 5.0, -5.0, 9.5, 3.14159]; RlOut(0, Mean(Test, 6)); CrLf(0); ]</lang>
Output:
2.60693
Yorick
<lang yorick>func mean(x) {
if(is_void(x)) return 0; return x(*)(avg);
}</lang>
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