Averages/Arithmetic mean

Averages/Arithmetic mean
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. The program should work on a zero-length vector (with an answer of 0).

Ada

This example shows how to pass a zero length vector as well as a larger vector.

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;

Output:

3.83333
0.00000

ALGOL 68

Translation of: C

Works with: ALGOL 68 version Standard - no extensions to language used

Works with: ALGOL 68G version Any - tested with release mk15-0.8b.fc9.i386

Works with: ELLA ALGOL 68 version Any (with appropriate job cards) - tested with release 1.8.8d.fc9.i386 - note that some necessary LONG REAL operators are missing from ELLA's library.

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))
)

AWK

<lang awk># work around a gawk bug in the length extended use:

1. so this is a more non-gawk compliant way to get
2. 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

Works with: APL2

      X←3 1 4 1 5 9
      (+/X)÷⍴X
3.833333333

BASIC

Works with: QuickBasic version 4.5

Assume the numbers are in a DIM named nums.

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

C

This implementation uses a plain old static array of doubles for the numeric vector.

<lang c>#include <stdio.h>

double mean(double *p, unsigned qty) /* Calculates the mean of qty doubles beginning at p. */

{if (qty == 0) return 0;
 double total = 0;
 for (int i = 0 ; i < qty ; ++i) total += p[i];
 return total / qty;}

int main(void)

{double test[6] = {1.0, 2.0, 5.0, -5.0, 9.5, 3.14159};
 printf("%lg\n", mean(test, 6));
 return 0;}</lang>

C++

Library: STL

<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>

1. 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>

C#

<lang csharp>using System.Linq;

static double avg(ICollection<int> i) {

   if (i == null || i.Count == 0) return 0;
   return i.Sum() / (double)i.Count;

}

static void Main(string[] args) {

   int[] numbers = new int[] {1, 2, 3, 4, 5, 6, 7, 8};           
   Console.WriteLine(avg(numbers));

}</lang>

C# already has a builtin Average function.

<lang csharp>static void Main(string[] args) {

   int[] numbers = new int[] {1, 2, 3, 4, 5, 6, 7, 8};           
   Console.WriteLine(numbers.Average());

}</lang>

Common Lisp

(defun mean (sequence)
  (let ((length (length sequence)))
    (if (zerop length)
      0
      (/ (reduce #'+ sequence) length))))

D

Using template to make the mean function work for higher-rank array.

module mean ;
import std.stdio ;

real mean(T)(T[] a) {
  static if(is(T U : U[])) {
    // recursively unfold the multi-array
    T u ;
    foreach(e ; a)
      u ~= e ;
    return u.mean() ;   

  } else {
    // do the math
    if(a.length == 0) return 0.0 ;
    real sum = 0.0 ;
    foreach(e ; a)
      sum += e ;
    return sum / a.length ;    
  }
}
void main() {
  int[] array = [3,1,4,1,5,9];    
  real[][][] 
    multi = [[[1,2,2],[2,3,4],[4,5,7]],
            [[4,1,3],[0,3,1],[4,4,6]],
            [[1,3,3],[2,7,8],[9,1,5]]] ;
  writefln("array : ", array.mean()) ;
  writefln("multi : ", multi.mean()) ;
}

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>

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>

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:

mean :: (Fractional a) => [a] -> a
mean [] = 0
mean xs = sum xs / Data.List.genericLength xs

But some types, e.g. integers, are not Fractional; the following function works for all Real types:

meanReals :: (Real a, Fractional b) => [a] -> b
meanReals = mean . map realToFrac

IDL

If truly only the mean is wanted, one could use

 x = [3,1,4,1,5,9]
 print,mean(x)

But mean() is just a thin wrapper returning the zeroth element of moment() :

print,moment(x)
; ==>
  3.83333      8.96667     0.580037     -1.25081

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

mean=: +/ % #

That is, sum divided by the number of items. The verb also works on higher-ranked arrays. For example:

   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

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.

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

Java

Assume the numbers are in a double array called "nums".

...
double mean = 0;
double sum = 0;
for(double i : nums){
  sum += i;
}
System.out.println("The mean is: " + ((nums.length != 0) ? (sum / nums.length) : 0));
...

JavaScript

function mean(array) {
  var sum = 0;
  for(var i in array)
    sum += array[i];
  return array.length ? sum / array.length : 0;
}

alert( mean( [1,2,3,4,5] ) );   // 3

Library: Functional

function mean(a) {
  return a.length ? Functional.reduce('+', 0, a) / a.length : 0;
}

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

Lucid

[1]

avg(x)
 where 
    sum = first(x) fby sum + next(x);
    n = 1 fby n + 1;
    avg = sum / n;
 end

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>

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))

Nial

in the standard way, mean is

mean is / [sum, tally] 

mean 6 2 4 
= 4

but it fails with 0 length vectors. so using a tally with a minimum value 1

dtally is recur [ empty rest, 1 first, 1 first, plus, rest ]
mean is / [sum, dtally]

mean []
=0

OCaml

These functions return a float:

<lang ocaml>let mean_floats xs =

 if xs = [] then
   0.
 else
   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 which 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 the order is not important, you can use List.rev_map instead to save an internal 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>

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>

Library: Data::AverageAverage

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>

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>

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;

Python

Works with: Python version 3.0

.

Works with: Python version 2.6

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([3,1,4,1,5,9])) print (average([1e20,3,1,4,1,5,9,-1e20]))</lang>

Output:

<lang python>3.83333333333333

2.875</lang>

Works with: Python version 2.5

<lang python>def average(x):

   return sum(x)/float(len(x)) if x else 0

print average([3,1,4,1,5,9]) print average([1e20,3,1,4,1,5,9,-1e20])</lang>

Output

(Notice how the second call gave the wrong result)

<lang python>3.83333333333333

0.0 </lang>

Works with: Python version 2.4

<lang python>def avg(data):
    if len(data)==0:
        return 0
    else:
        return sum(data)/float(len(data))
print avg([3,1,4,1,5,9])</lang>

Output:

<lang python>3.83333333333333</lang>

Ruby

<lang ruby>nums = [3, 1, 4, 1, 5, 9] nums.empty? ? 0 : nums.inject(:+) / Float(nums.size)</lang>

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

Smalltalk

<lang smalltalk>| numbers | numbers := #(1 2 3 4 5 6 7 8). (numbers isEmpty ifTrue:[0]

                ifFalse: [
                  (numbers inject: 0 into: [:sum :aNumber | sum + aNumber]) / numbers size
                ]

) displayNl.</lang>

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 which 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>

UnixPipes

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

V

[mean
   [sum 0 [+] fold].
   dup sum
   swap size [[1 <] [1]] when /
].