Averages/Root mean square: Difference between revisions

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Task

Compute the Root mean square of the numbers 1..10.

The root mean square is also known by its initials RMS (or rms), and as the quadratic mean.

The RMS is calculated as the mean of the squares of the numbers, square-rooted:

x_{\mathrm {rms} }={\sqrt {{{x_{1}}^{2}+{x_{2}}^{2}+\cdots +{x_{n}}^{2}} \over n}}.

11l

Translation of: Python

<lang 11l>F qmean(num)

  R sqrt(sum(num.map(n -> n * n)) / Float(num.len))

print(qmean(1..10))</lang>

Output:

6.20484

Ada

<lang Ada>with Ada.Float_Text_IO; use Ada.Float_Text_IO; with Ada.Numerics.Elementary_Functions; use Ada.Numerics.Elementary_Functions; procedure calcrms is type float_arr is array(1..10) of Float;

function rms(nums : float_arr) return Float is sum : Float := 0.0; begin for p in nums'Range loop sum := sum + nums(p)**2; end loop; return sqrt(sum/Float(nums'Length)); end rms;

list : float_arr; begin list := (1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0,9.0,10.0); put( rms(list) , Exp=>0); end calcrms;</lang>

Output:

 6.20484

ALGOL 68

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

Works with: ALGOL 68G version Any - tested with release 1.18.0-9h.tiny

Works with: ELLA ALGOL 68 version Any (with appropriate job cards)

<lang algol68># Define the rms PROCedure & ABS OPerators for LONG... REAL # MODE RMSFIELD = #LONG...# REAL; PROC (RMSFIELD)RMSFIELD rms field sqrt = #long...# sqrt; INT rms field width = #long...# real width;

PROC crude rms = ([]RMSFIELD v)RMSFIELD: (

 RMSFIELD sum := 0;
 FOR i FROM LWB v TO UPB v DO sum +:= v[i]**2 OD;
 rms field sqrt(sum / (UPB v - LWB v + 1))

);

PROC rms = ([]RMSFIELD v)RMSFIELD: (

round off error accumulated at standard precision #

 RMSFIELD sum := 0, round off error:= 0;
 FOR i FROM LWB v TO UPB v DO 
   RMSFIELD org = sum, prod = v[i]**2;
   sum +:= prod;
   round off error +:= sum - org - prod
 OD;
 rms field sqrt((sum - round off error)/(UPB v - LWB v + 1))

);

main: (

 []RMSFIELD one to ten = (1,2,3,4,5,6,7,8,9,10);

 print(("crude rms(one to ten): ", crude rms(one to ten), new line));
 print(("rms(one to ten): ",       rms(one to ten), new line))

)</lang>

Output:

crude rms(one to ten): +6.20483682299543e  +0
rms(one to ten): +6.20483682299543e  +0

ALGOL-M

Because ALGOL-M lacks a built-in square root function, we have to supply our own. <lang algol> BEGIN

DECIMAL FUNCTION SQRT(X); DECIMAL X; BEGIN

   DECIMAL R1, R2, TOL;
   TOL := .00001;   % reasonable for most purposes %
   IF X >= 1.0 THEN
      BEGIN
         R1 := X;
         R2 := 1.0;
      END
   ELSE
      BEGIN
         R1 := 1.0;
         R2 := X;
      END;
   WHILE (R1-R2) > TOL DO
       BEGIN
           R1 := (R1+R2) / 2.0;
           R2 := X / R1;
       END;
   SQRT := R1;

END;

COMMENT - MAIN PROGRAM BEGINS HERE;

DECIMAL N, SQSUM, SQMEAN;

SQSUM := 0.0; FOR N := 1.0 STEP 1.0 UNTIL 10.0 DO

   SQSUM := SQSUM + (N * N);

SQMEAN := SQSUM / (N - 1.0); WRITE("RMS OF WHOLE NUMBERS 1.0 THROUGH 10.0 =", SQRT(SQMEAN));

END</lang>

Output:

Based on the limited precision of the square root function, only the first six decimal places of the output can actually be relied on (but that's more than sufficient for most real world uses).

RMS OF WHOLE NUMBERS 1.0 THROUGH 10.0 = 6.20483683432

ALGOL W

<lang algolw>begin

   % computes the root-mean-square of an array of numbers with               %
   % the specified lower bound (lb) and upper bound (ub)                     %
   real procedure rms( real    array numbers ( * )
                     ; integer value lb
                     ; integer value ub
                     ) ;
       begin
           real sum;
           sum := 0;
           for i := lb until ub do sum := sum + ( numbers(i) * numbers(i) );
           sqrt( sum / ( ( ub - lb ) + 1 ) )
       end rms ;

   % test the rms procedure with the numbers 1 to 10                         %
   real array testNumbers( 1 :: 10 );
   for i := 1 until 10 do testNumbers(i) := i;
   r_format := "A"; r_w := 10; r_d := 4; % set fixed point output           %
   write( "rms of 1 .. 10: ", rms( testNumbers, 1, 10 ) );

end.</lang>

Output:

rms of 1 .. 10:     6.2048

APL

<lang APL> rms←{((+/⍵*2)÷⍴⍵)*0.5}

x←⍳10

rms x

6.204836823</lang>

AppleScript

Translation of: JavaScript

( ES6 version )

<lang AppleScript>-- rootMeanSquare :: [Num] -> Real on rootMeanSquare(xs)

   script
       on |λ|(a, x)
           a + x * x
       end |λ|
   end script
   
   (foldl(result, 0, xs) / (length of xs)) ^ (1 / 2)

end rootMeanSquare

-- TEST ----------------------------------------------------------------------- on run

   rootMeanSquare({1, 2, 3, 4, 5, 6, 7, 8, 9, 10})
   
   -- > 6.204836822995

end run

-- GENERIC FUNCTIONS ----------------------------------------------------------

-- foldl :: (a -> b -> a) -> a -> [b] -> a on foldl(f, startValue, xs)

   tell mReturn(f)
       set v to startValue
       set lng to length of xs
       repeat with i from 1 to lng
           set v to |λ|(v, item i of xs, i, xs)
       end repeat
       return v
   end tell

end foldl

-- Lift 2nd class handler function into 1st class script wrapper -- mReturn :: Handler -> Script on mReturn(f)

   if class of f is script then
       f
   else
       script
           property |λ| : f
       end script
   end if

end mReturn</lang>

Output:

6.204836822995

Astro

AutoHotkey

Using a loop

<lang autohotkey>MsgBox, % RMS(1, 10)

---------------------------------------------------------------------------

RMS(a, b) { ; Root Mean Square of integers a through b

---------------------------------------------------------------------------

   n := b - a + 1
   Loop, %n%
       Sum += (a + A_Index - 1) ** 2
   Return, Sqrt(Sum / n)

}</lang> Message box shows:

6.204837

Avoiding a loop

Using these equations:
$\sum _{i=1}^{n}i^{2}={\frac {n(n+1)(2n+1)}{6}}$ See wp:List of mathematical series

for $a<b$ : $\sum _{i=a}^{b}i^{2}=\sum _{i=1}^{b}i^{2}-\sum _{i=1}^{a-1}i^{2}$

We can show that:
$\sum _{i=a}^{b}i^{2}={\frac {b(b+1)(2b+1)-a(a-1)(2a-1)}{6}}$ <lang autohotkey>MsgBox, % RMS(1, 10)

---------------------------------------------------------------------------

RMS(a, b) { ; Root Mean Square of integers a through b

---------------------------------------------------------------------------

   Return, Sqrt((b*(b+1)*(2*b+1)-a*(a-1)*(2*a-1))/6/(b-a+1))

}</lang> Message box shows:

6.204837

AWK

<lang awk>#!/usr/bin/awk -f

computes RMS of the 1st column of a data file

{

   x  = $1;   # value of 1st column
   S += x*x;  
   N++;

}

END {

  print "RMS: ",sqrt(S/N);

}</lang>

BASIC

Works with: QBasic

Note that this will work in Visual Basic and the Windows versions of PowerBASIC by simply wrapping the module-level code into the MAIN function, and changing PRINT to MSGBOX.

<lang qbasic>DIM i(1 TO 10) AS DOUBLE, L0 AS LONG FOR L0 = 1 TO 10

   i(L0) = L0

NEXT PRINT STR$(rms#(i()))

FUNCTION rms# (what() AS DOUBLE)

   DIM L0 AS LONG, tmp AS DOUBLE, rt AS DOUBLE
   FOR L0 = LBOUND(what) TO UBOUND(what)
       rt = rt + (what(L0) ^ 2)
   NEXT
   tmp = UBOUND(what) - LBOUND(what) + 1
   rms# = SQR(rt / tmp)

END FUNCTION</lang>

Applesoft BASIC

<lang ApplesoftBasic> 10 N = 10

20  FOR I = 1 TO N
30 S = S + I * I
40  NEXT
50 X =  SQR (S / N)
60  PRINT X</lang>

Output:

6.20483683

IS-BASIC

<lang IS-BASIC>100 PRINT RMS(10) 110 DEF RMS(N) 120 LET R=0 130 FOR X=1 TO N 140 LET R=R+X^2 150 NEXT 160 LET RMS=SQR(R/N) 170 END DEF</lang>

Sinclair ZX81 BASIC

<lang basic>10 FAST 20 LET RMS=0 30 FOR X=1 TO 10 40 LET RMS=RMS+X**2 50 NEXT X 60 LET RMS=SQR (RMS/10) 70 SLOW 80 PRINT RMS</lang>

Output:

6.2048368

BBC BASIC

<lang bbcbasic> DIM array(9)

     array() = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
     
     PRINT FNrms(array())
     END
     
     DEF FNrms(a()) = MOD(a()) / SQR(DIM(a(),1)+1)</lang>

C

<lang c>#include <stdio.h>

include <math.h>

double rms(double *v, int n) {

 int i;
 double sum = 0.0;
 for(i = 0; i < n; i++)
   sum += v[i] * v[i];
 return sqrt(sum / n);

}

int main(void) {

 double v[] = {1., 2., 3., 4., 5., 6., 7., 8., 9., 10.};
 printf("%f\n", rms(v, sizeof(v)/sizeof(double)));
 return 0;

}</lang>

C#

<lang csharp>using System;

namespace rms {

   class Program
   {
       static void Main(string[] args)
       {
           int[] x = new int[] { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 };
           Console.WriteLine(rootMeanSquare(x));
       }

       private static double rootMeanSquare(int[] x)
       {            
           double sum = 0;
           for (int i = 0; i < x.Length; i++)
           {
               sum += (x[i]*x[i]);
           }
           return Math.Sqrt(sum / x.Length);
       }
   }

}</lang> An alternative method demonstrating the more functional style introduced by LINQ and lambda expressions in C# 3.

Works with: C# version 3

<lang csharp>using System; using System.Collections.Generic; using System.Linq;

namespace rms {

   class Program
   {
       static void Main(string[] args)
       {
           Console.WriteLine(rootMeanSquare(Enumerable.Range(1, 10)));
       }

       private static double rootMeanSquare(IEnumerable<int> x)
       {
           return Math.Sqrt(x.Average(i => (double)i * i));
       }
   }

}</lang>

C++

<lang Cpp>#include <iostream>

include <vector>
include <cmath>
include <numeric>

int main( ) {

 std::vector<int> numbers ;
 for ( int i = 1 ; i < 11 ; i++ )
   numbers.push_back( i ) ;
 double meansquare = sqrt( ( std::inner_product( numbers.begin(), numbers.end(), numbers.begin(), 0 ) ) / static_cast<double>( numbers.size() ) );
 std::cout << "The quadratic mean of the numbers 1 .. " << numbers.size() << " is " << meansquare << " !\n" ;
 return 0 ;

}</lang>

Output:

The quadratic mean of the numbers 1 .. 10 is 6.20484 !

Clojure

<lang clojure> (defn rms [xs]

 (Math/sqrt (/ (reduce + (map #(* % %) xs))

(count xs))))

(println (rms (range 1 11)))</lang>

Output:

6.2048368229954285

COBOL

Could be written more succinctly, with an inline loop and more COMPUTE statements; but that wouldn't be very COBOLic. <lang cobol>IDENTIFICATION DIVISION. PROGRAM-ID. QUADRATIC-MEAN-PROGRAM. DATA DIVISION. WORKING-STORAGE SECTION. 01 QUADRATIC-MEAN-VARS.

   05 N               PIC 99        VALUE 0.
   05 N-SQUARED       PIC 999.
   05 RUNNING-TOTAL   PIC 999       VALUE 0.
   05 MEAN-OF-SQUARES PIC 99V9(16).
   05 QUADRATIC-MEAN  PIC 9V9(15).

PROCEDURE DIVISION. CONTROL-PARAGRAPH.

   PERFORM MULTIPLICATION-PARAGRAPH 10 TIMES.
   DIVIDE  RUNNING-TOTAL BY 10 GIVING MEAN-OF-SQUARES.
   COMPUTE QUADRATIC-MEAN = FUNCTION SQRT(MEAN-OF-SQUARES).
   DISPLAY QUADRATIC-MEAN UPON CONSOLE.
   STOP RUN.

MULTIPLICATION-PARAGRAPH.

   ADD      1         TO N.
   MULTIPLY N         BY N GIVING N-SQUARED.
   ADD      N-SQUARED TO RUNNING-TOTAL.</lang>

Output:

6.204836822995428

CoffeeScript

Translation of: JavaScript

<lang coffeescript> root_mean_square = (ary) ->

       sum_of_squares = ary.reduce ((s,x) -> s + x*x), 0
       return Math.sqrt(sum_of_squares / ary.length)
    
   alert root_mean_square([1..10])</lang>

Common Lisp

<lang lisp>(loop for x from 1 to 10

     for xx = (* x x)
     for n from 1
     summing xx into xx-sum
     finally (return (sqrt (/ xx-sum n))))</lang>

Here's a non-iterative solution.

<lang lisp> (defun root-mean-square (numbers)

 "Takes a list of numbers, returns their quadratic mean."
 (sqrt
  (/ (apply #'+ (mapcar #'(lambda (x) (* x x)) numbers))
     (length numbers))))

(root-mean-square (loop for i from 1 to 10 collect i)) </lang>

Crystal

Translation of: Ruby

<lang ruby>def rms(seq)

 Math.sqrt(seq.sum { |x| x*x } / seq.size)

end

puts rms (1..10).to_a</lang>

Output:

6.2048368229954285

D

<lang d>import std.stdio, std.math, std.algorithm, std.range;

real rms(R)(R d) pure {

   return sqrt(d.reduce!((a, b) => a + b * b) / real(d.length));

}

void main() {

   writefln("%.19f", iota(1, 11).rms);

}</lang>

Output:

6.2048368229954282979

Delphi/Pascal

<lang Delphi>program AveragesMeanSquare;

{$APPTYPE CONSOLE}

uses Types;

function MeanSquare(aArray: TDoubleDynArray): Double; var

 lValue: Double;

begin

 Result := 0;

 for lValue in aArray do
   Result := Result + (lValue * lValue);
 if Result > 0 then
   Result := Sqrt(Result / Length(aArray));

end;

begin

 Writeln(MeanSquare(TDoubleDynArray.Create()));
 Writeln(MeanSquare(TDoubleDynArray.Create(1,2,3,4,5,6,7,8,9,10)));

end.</lang>

E

Using the same generic mean function as used in pythagorean means: <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 RMS := makeMean(0, fn b,x { b+x**2 }, fn acc,n { (acc/n).sqrt() })</lang>

<lang e>? RMS(1..10)

value: 6.2048368229954285</lang>

EchoLisp

<lang scheme> (define (rms xs)

   (sqrt (// (for/sum ((x xs)) (* x x)) (length xs))))

(rms (range 1 11))

   → 6.2048368229954285

</lang>

Elena

Translation of: C#

ELENA 5.0 : <lang elena>import extensions; import system'routines; import system'math;

extension op {

   get RootMeanSquare()
       = (self.selectBy:(x => x * x).summarize(Real.new()) / self.Length).sqrt();

}

public program() {

   console.printLine(new Range(1, 10).RootMeanSquare)

}</lang>

Output:

6.204836822995

Elixir

<lang elixir> defmodule RC do

 def root_mean_square(enum) do
   enum
   |> square
   |> mean
   |> :math.sqrt
 end

 defp mean(enum), do: Enum.sum(enum) / Enum.count(enum)

 defp square(enum), do: (for x <- enum, do: x * x)

end

IO.puts RC.root_mean_square(1..10) </lang>

Output:

6.2048368229954285

Emacs Lisp

<Lang lisp> (defun rms (nums)

 ;; `/' returns a float only when given floats
 (setq nums (mapcar 'float nums))
 (sqrt (/ (apply '+ (mapcar (lambda (x) (* x x)) nums))

(length nums)))) </lang>

or, if using Emacs's Common Lisp library cl-lib.el to use cl-map: <Lang lisp> (defun rms (nums)

 (setq nums (mapcar 'float nums))
 (sqrt (/ (apply '+ (cl-map 'list '* nums nums))

(length nums))))

(rms (number-sequence 1 10)) </lang>

6.2048368229954285

Erlang

   math:sqrt(lists:foldl(fun(E,S) -> S+E*E end, 0, Nums) / length(Nums)).

rms([1,2,3,4,5,6,7,8,9,10]).</lang>

Output:

6.2048368229954285

ERRE

<lang> PROGRAM ROOT_MEAN_SQUARE BEGIN

 N=10
 FOR I=1 TO N DO
    S=S+I*I
 END FOR
 X=SQR(S/N)
 PRINT("Root mean square is";X)

END PROGRAM </lang> You can, obviously, generalize reading data from a DATA line or from a file.

Euphoria

<lang euphoria>function rms(sequence s)

   atom sum
   if length(s) = 0 then
       return 0
   end if
   sum = 0
   for i = 1 to length(s) do
       sum += power(s[i],2)
   end for
   return sqrt(sum/length(s))

end function

constant s = {1,2,3,4,5,6,7,8,9,10} ? rms(s)</lang>

Output:

6.204836823

Excel

If values are entered in the cells A1 to A10, the below expression will give the RMS value <lang excel> =SQRT(SUMSQ($A1:$A10)/COUNT($A1:$A10)) </lang>

The RMS of [1,10] is then : 6.204836823 ( Actual displayed value 6.204837)

F#

Uses a lambda expression and function piping. <lang Fsharp>let RMS (x:float list) : float = List.map (fun y -> y**2.0) x |> List.average |> System.Math.Sqrt

let res = RMS [1.0..10.0]</lang> Answer (in F# Interactive window):

val res : float = 6.204836823

Factor

<lang factor>: root-mean-square ( seq -- mean )

   [ [ sq ] map-sum ] [ length ] bi / sqrt ;</lang>

( scratchpad ) 10 [1,b] root-mean-square .
6.204836822995428

Fantom

<lang fantom>class Main {

 static Float averageRms (Float[] nums)
 {
   if (nums.size == 0) return 0.0f
   Float sum := 0f
   nums.each { sum += it * it }
   return (sum / nums.size.toFloat).sqrt
 }

 public static Void main ()
 {
   a := [1f,2f,3f,4f,5f,6f,7f,8f,9f,10f]
   echo ("RMS Average of $a is: " + averageRms(a))
 }

}</lang>

Forth

<lang forth>: rms ( faddr len -- frms )

 dup >r 0e
 floats bounds do
   i f@ fdup f* f+
 float +loop
 r> s>f f/ fsqrt ;

create test 1e f, 2e f, 3e f, 4e f, 5e f, 6e f, 7e f, 8e f, 9e f, 10e f, test 10 rms f. \ 6.20483682299543</lang>

Fortran

Assume $x$ stored in array x. <lang Fortran>print *,sqrt( sum(x**2)/size(x) )</lang>

FreeBASIC

<lang freebasic> ' FB 1.05.0 Win64

Function QuadraticMean(array() As Double) As Double

 Dim length As Integer = Ubound(array) - Lbound(array) + 1
 Dim As Double sum = 0.0
 For i As Integer = LBound(array) To UBound(array)
   sum += array(i) * array(i)
 Next
 Return Sqr(sum/length)

End Function

Dim vector(1 To 10) As Double For i As Integer = 1 To 10

 vector(i) = i

Output:

Quadratic mean (or RMS) is : 6.204836822995429

Futhark

<lang Futhark> import "futlib/math"

fun main(as: [n]f64): f64 =

 f64.sqrt ((reduce (+) 0.0 (map (**2.0) as)) / f64(n))

</lang>

GEORGE

<lang GEORGE> 1, 10 rep (i)

  i i | (v) ;

0

1, 10 rep (i)
  i dup mult +
  ]

10 div

sqrt
print

</lang>

 6.204836822995428

Go

<lang go>package main

import (

   "fmt"
   "math"

)

func main() {

   const n = 10
   sum := 0.
   for x := 1.; x <= n; x++ {
       sum += x * x
   }
   fmt.Println(math.Sqrt(sum / n))

}</lang>

Output:

6.2048368229954285

Groovy

Solution: <lang groovy>def quadMean = { list ->

   list == null \
       ? null \
       : list.empty \
           ? 0 \
           : ((list.collect { it*it }.sum()) / list.size()) ** 0.5

}</lang> Test: <lang groovy>def list = 1..10 def Q = quadMean(list) println """ list: ${list}

  Q: ${Q}

"""</lang>

Output:

list: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
   Q: 6.2048368229954285

Haskell

Given the mean function defined in Averages/Pythagorean means: <lang haskell>main = print $ mean 2 [1 .. 10]</lang>

Or, writing a naive mean of our own, (but see https://donsbot.wordpress.com/2008/06/04/haskell-as-fast-as-c-working-at-a-high-altitude-for-low-level-performance/):

<lang haskell>import Data.List (genericLength)

rootMeanSquare :: [Double] -> Double rootMeanSquare = sqrt . (((/) . foldr ((+) . (^ 2)) 0) <*> genericLength)

main :: IO () main = print $ rootMeanSquare [1 .. 10]</lang>

Output:

6.2048368229954285

HicEst

<lang HicEst>sum = 0 DO i = 1, 10

  sum = sum + i^2

ENDDO WRITE(ClipBoard) "RMS(1..10) = ", (sum/10)^0.5 </lang> RMS(1..10) = 6.204836823

Icon and Unicon

<lang Icon>procedure main() every put(x := [], 1 to 10) writes("x := [ "); every writes(!x," "); write("]") write("Quadratic mean:",q := qmean!x) end</lang>

<lang Icon>procedure qmean(L[]) #: quadratic mean

  local m
  if *L = 0 then fail
  every (m := 0.0) +:= !L^2
  return sqrt(m / *L)

end</lang>

Io

<lang Io>rms := method (figs, (figs map(** 2) reduce(+) / figs size) sqrt)

rms( Range 1 to(10) asList ) println</lang>

J

Solution: <lang j>rms=: (+/ % #)&.:*:</lang>

Example Usage: <lang j> rms 1 + i. 10 6.20484</lang> *: means square

(+/ % #) is an idiom for mean.

&.: means under -- in other words, we square numbers, take their average and then use the inverse of square on the result. (see also the page on &. which does basically the same thing but with different granularity -- item at a time instead of everything at once.

Java

<lang java>public class RootMeanSquare {

   public static double rootMeanSquare(double... nums) {
       double sum = 0.0;
       for (double num : nums)
           sum += num * num;
       return Math.sqrt(sum / nums.length);
   }

   public static void main(String[] args) {
       double[] nums = {1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0};
       System.out.println("The RMS of the numbers from 1 to 10 is " + rootMeanSquare(nums));
   }

}</lang>

Output:

The RMS of the numbers from 1 to 10 is 6.2048368229954285

JavaScript

ES5

Works with: JavaScript version 1.8

Works with: Firefox version 3.0

<lang javascript>function root_mean_square(ary) {

   var sum_of_squares = ary.reduce(function(s,x) {return (s + x*x)}, 0);
   return Math.sqrt(sum_of_squares / ary.length);

}

print( root_mean_square([1,2,3,4,5,6,7,8,9,10]) ); // ==> 6.2048368229954285</lang>

ES6

<lang JavaScript>(() => {

   'use strict';


   // rootMeanSquare :: [Num] -> Real
   const rootMeanSquare = xs => 
      Math.sqrt(
           xs.reduce(
               (a, x) => (a + x * x),
               0
          ) / xs.length
       );

    
   return rootMeanSquare([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]);
   
    // -> 6.2048368229954285

})();</lang>

Output:

6.2048368229954285

jq

The following filter returns null if given an empty array: <lang jq>def rms: length as $length

 | if $length == 0 then null
   else map(. * .) | add | sqrt / $length
   end ;</lang>With this definition, the following program would compute the rms of each array in a file or stream of numeric arrays:<lang jq>rms</lang>

Julia

There are a variety of ways to do this via built-in functions in Julia, given an array A = [1:10] of values. The formula can be implemented directly as: <lang julia>sqrt(sum(A.^2.) / length(A))</lang> or shorter with using Statistics (and as spoken: root-mean-square) <lang julia>sqrt(mean(A.^2.))</lang> or the implicit allocation of a new array by A.^2. can be avoided by using sum as a higher-order function: <lang julia>sqrt(sum(x -> x*x, A) / length(A))</lang> One can also use an explicit loop for near-C performance <lang julia> function rms(A)

  s = 0.0
  for a in A
     s += a*a
  end
  return sqrt(s / length(A))

end </lang> Potentially even better is to use the built-in norm function, which computes the square root of the sum of the squares of the entries of A in a way that avoids the possibility of spurious floating-point overflow (if the entries of A are so large that they may overflow if squared): <lang julia>norm(A) / sqrt(length(A))</lang>

K

 rms:{_sqrt (+/x^2)%#x}
 rms 1+!10

6.204837 </lang>

Kotlin

<lang scala>// version 1.0.5-2

fun quadraticMean(vector: Array<Double>) : Double {

   val sum = vector.sumByDouble { it * it }
   return Math.sqrt(sum / vector.size)

}

fun main(args: Array<String>) {

   val vector = Array(10, { (it + 1).toDouble() })
   print("Quadratic mean of numbers 1 to 10 is ${quadraticMean(vector)}")

}</lang>

Output:

Quadratic mean of numbers 1 to 10 is 6.2048368229954285

Lasso

<lang Lasso>define rms(a::staticarray)::decimal => { return math_sqrt((with n in #a sum #n*#n) / decimal(#a->size)) } rms(generateSeries(1,10)->asStaticArray)</lang>

Output:

6.204837

Liberty BASIC

<lang lb>' [RC] Averages/Root mean square

   SourceList$     ="1 2 3 4 5 6 7 8 9 10"

   '   If saved as an array we'd have to have a flag for last data.
   '   LB has the very useful word$() to read from delimited strings.
   '   The default delimiter is a space character, " ".

   SumOfSquares    =0
   n               =0      '   This holds index to number, and counts number of data.
   data$           ="666"  '   temporary dummy to enter the loop.

   while data$ <>""                                '   we loop until no data left.
       data$           =word$( SourceList$, n +1)  '   first data, as a string
       NewVal          =val( data$)                '   convert string to number
       SumOfSquares    =SumOfSquares +NewVal^2     '   add to existing sum of squares
       n =n +1                                     '   increment number of data items found
   wend

   n =n -1

   print "Supplied data was ";         SourceList$
   print "This contained ";            n; " numbers."
   print "R.M.S. value is ";           ( SumOfSquares /n)^0.5

   end</lang>

Logo

<lang logo>to rms :v

 output sqrt quotient (apply "sum map [? * ?] :v) count :v

end

show rms iseq 1 10</lang>

Lua

<lang lua>function sumsq(a, ...) return a and a^2 + sumsq(...) or 0 end function rms(t) return (sumsq(unpack(t)) / #t)^.5 end

print(rms{1, 2, 3, 4, 5, 6, 7, 8, 9, 10})</lang>

Maple

<lang Maple>y := [ seq(1..10) ]: RMS := proc( x )

   return sqrt( Statistics:-Mean( x ^~ 2 ) );

end proc: RMS( y ); </lang>

Output:

6.20483682299543

Mathematica / Wolfram Language

<lang Mathematica>RootMeanSquare@Range[10]</lang> The above will give the precise solution ${\sqrt {\frac {77}{2}}}$ , to downgrade to 6.20484, use '10.' to imply asking for numeric solution, or append '//N' after the whole expression.

MATLAB

<lang MATLAB>function rms = quadraticMean(list)

   rms = sqrt(mean(list.^2));

end</lang> Solution: <lang MATLAB>>> quadraticMean((1:10))

ans =

  6.204836822995429</lang>

Maxima

<lang maxima>L: makelist(i, i, 10)$

rms(L) := sqrt(lsum(x^2, x, L)/length(L))$

rms(L), numer; /* 6.204836822995429 */</lang>

MAXScript

<lang MAXScript> fn RMS arr = ( local sumSquared = 0 for i in arr do sumSquared += i^2 return (sqrt (sumSquared/arr.count as float)) ) </lang> Output: <lang MAXScript> rms #{1..10} 6.20484 </lang>

min

Works with: min version 0.19.6

<lang min>(dup *) :sq ('sq map sum) :sum-sq (('sum-sq 'size) => cleave / sqrt) :rms

(1 2 3 4 5 6 7 8 9 10) rms puts!</lang>

Output:

6.204836822995429

МК-61/52

<lang>0 П0 П1 С/П x^2 ИП0 x^2 ИП1 * + ИП1 1 + П1 / КвКор 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.

Morfa

Translation of: D

<lang morfa> import morfa.base; import morfa.functional.base;

template <TRange> func rms(d: TRange): float {

   var count = 1;
   return sqrt(reduce( (a: float, b: float) { count += 1; return a + b * b; }, d) / count);

}

func main(): void {

   println(rms(1 .. 11));

} </lang>

Output:

6.204837

Nemerle

<lang Nemerle>using System; using System.Console; using System.Math;

module RMS {

   RMS(x : list[int]) : double
   {
       def sum = x.Map(fun (x) {x*x}).FoldLeft(0, _+_);
       Sqrt((sum :> double) / x.Length)
   }
   
   Main() : void
   {
       WriteLine("RMS of [1 .. 10]: {0:g6}", RMS($[1 .. 10]));
   }

}</lang>

NetRexx

<lang NetRexx>/* NetRexx */ options replace format comments java crossref symbols nobinary

parse arg maxV . if maxV = | maxV = '.' then maxV = 10

sum = 0 loop nr = 1 for maxV

 sum = sum + nr ** 2
 end nr

rmsD = Math.sqrt(sum / maxV)

say 'RMS of values from 1 to' maxV':' rmsD

return </lang>

Output:

RMS of values from 1 to 10: 6.204836822995428

Nim

<lang nim>from math import sqrt, sum from sequtils import mapIt

proc qmean(num: seq[float]): float =

 result = num.mapIt(it * it).sum
 result = sqrt(result / float(num.len))

echo qmean(@[1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0,9.0,10.0])</lang>

Output:

6.2048368229954285e+00

Oberon-2

Oxford Oberon-2 <lang oberon2> MODULE QM; IMPORT ML := MathL, Out; VAR nums: ARRAY 10 OF LONGREAL; i: INTEGER;

PROCEDURE Rms(a: ARRAY OF LONGREAL): LONGREAL; VAR i: INTEGER; s: LONGREAL; BEGIN s := 0.0; FOR i := 0 TO LEN(a) - 1 DO s := s + (a[i] * a[i]) END; RETURN ML.Sqrt(s / LEN(a)) END Rms;

BEGIN FOR i := 0 TO LEN(nums) - 1 DO nums[i] := i + 1 END; Out.String("Quadratic Mean: ");Out.LongReal(Rms(nums));Out.Ln END QM. </lang>

Output:

Quadratic Mean: 6.20483682300

Objeck

<lang objeck>bundle Default {

 class Hello {
   function : Main(args : String[]) ~ Nil {
     values := [1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0];
     RootSquareMean(values)->PrintLine();
   }
   
   function : native : RootSquareMean(values : Float[]) ~ Float {
     sum := 0.0;
     each(i : values) {
       x := values[i]->Power(2.0);
       sum += values[i]->Power(2.0);
     };
     
     return (sum / values->Size())->SquareRoot();
   }
 }

}</lang>

OCaml

<lang ocaml>let rms a =

 sqrt (Array.fold_left (fun s x -> s +. x*.x) 0.0 a /.
       float_of_int (Array.length a))

rms (Array.init 10 (fun i -> float_of_int (i+1))) ;; (* 6.2048368229954285 *)</lang>

Oforth

Output:

6.20483682299543

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(30, 10, 20, 30, 40, 50, -100, 4.7, -11e2)

routine testAverage

 use arg list
 say "list =" list~toString("l", ", ")
 say "root mean square =" rootmeansquare(list)
 say

routine rootmeansquare

 use arg numbers
 -- return zero for an empty list
 if numbers~isempty then return 0

 sum = 0
 do number over numbers
     sum += number * number
 end
 return rxcalcsqrt(sum/numbers~items)

requires rxmath LIBRARY</lang>

Output:

list = 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
root mean square = 6.20483682

list = 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 0, 0, .11
root mean square = 5.06630766

list = 30, 10, 20, 30, 40, 50, -100, 4.7, -1100
root mean square = 369.146476

Oz

<lang oz>declare

 fun {Square X} X*X end

 fun {RMS Xs}
    {Sqrt
     {Int.toFloat {FoldL {Map Xs Square} Number.'+' 0}}
     /
     {Int.toFloat {Length Xs}}}
 end

in

 {Show {RMS {List.number 1 10 1}}}</lang>

Output:

6.2048

PARI/GP

General RMS calculation: <lang parigp>RMS(v)={

 sqrt(sum(i=1,#v,v[i]^2)/#v)

};

RMS(vector(10,i,i))</lang>

Specific functions for the first n positive integers: <lang parigp>RMS_first(n)={

 sqrt((n+1)*(2*n+1)/6)

};

RMS_first(10)</lang> Asymptotically this is n/sqrt(3).

Perl

<lang perl>use v5.10.0; sub rms {

       my $r = 0;
       $r += $_**2 for @_;
       sqrt( $r/@_ );

}

say rms(1..10);</lang>

Phix

<lang Phix>function rms(sequence s) atom sqsum = 0

   for i=1 to length(s) do
       sqsum += power(s[i],2)
   end for
   return sqrt(sqsum/length(s))

end function

?rms({1,2,3,4,5,6,7,8,9,10})</lang>

Output:

6.204836823

Alternative, same output <lang Phix>function rms(sequence s)

   return sqrt(sum(apply(true,power,{s,2}))/length(s))

end function ?rms(tagset(10))</lang>

Phixmonti

<lang Phixmonti>def rms

   0 swap
   len for
       get 2 power rot + swap
   endfor
   len rot swap / sqrt

enddef

0 tolist 10 for

   0 put

endfor

rms print</lang>

PHP

<lang PHP><?php // Created with PHP 7.0

function rms(array $numbers) {

   $sum = 0;

   foreach ($numbers as $number) {
       $sum += $number**2;
   }

   return sqrt($sum / count($numbers));

}

echo rms(array(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)); </lang>

Output:

6.2048368229954

PicoLisp

<lang PicoLisp>(scl 5)

(let Lst (1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0)

  (prinl
     (format
        (sqrt
           (*/
              (sum '((N) (*/ N N 1.0)) Lst)
              1.0
              (length Lst) )
           T )
        *Scl ) ) )</lang>

Output:

6.20484

PL/I

<lang PL/I> atest: Proc Options(main);

declare A(10) Dec Float(15) static initial (1,2,3,4,5,6,7,8,9,10);
declare (n,RMS) Dec Float(15);
n = hbound(A,1);
RMS = sqrt(sum(A**2)/n);
put Skip Data(rms);
End;</lang>

Output:

RMS= 6.20483682299543E+0000;

PostScript

<lang postscript>/findrms{ /x exch def /sum 0 def /i 0 def x length 0 eq{} { x length{ /sum x i get 2 exp sum add def /i i 1 add def }repeat /sum sum x length div sqrt def }ifelse sum == }def

[1 2 3 4 5 6 7 8 9 10] findrms</lang>

Output:

6.20483685

Library: initlib

<lang postscript>[1 10] 1 range dup 0 {dup * +} fold exch length div sqrt</lang>

Potion

<lang Potion>rms = (series) :

  total = 0.0
  series each (x): total += x * x.
  total /= series length
  total sqrt

.

rms((1, 2, 3, 4, 5, 6, 7, 8, 9, 10)) print</lang>

Powerbuilder

<lang powerbuilder>long ll_x, ll_y, ll_product decimal ld_rms

ll_x = 1 ll_y = 10 DO WHILE ll_x <= ll_y ll_product += ll_x * ll_x ll_x ++ LOOP ld_rms = Sqrt(ll_product / ll_y)

//ld_rms value is 6.20483682299542849</lang>

PowerShell

<lang PowerShell>function get-rms([float[]]$nums){

  $sqsum=$nums | foreach-object { $_*$_} | measure-object -sum | select-object -expand Sum
  return [math]::sqrt($sqsum/$nums.count)

}

get-rms @(1..10) </lang>

PureBasic

<lang PureBasic>NewList MyList() ; To hold a unknown amount of numbers to calculate

If OpenConsole()

 Define.d result
 Define i, sum_of_squares
 
 ;Populate a random amounts of numbers to calculate
 For i=0 To (Random(45)+5) ; max elements is unknown to the program
   AddElement(MyList())
   MyList()=Random(15)  ; Put in a random number
 Next

 Print("Averages/Root mean square"+#CRLF$+"of : ")

 ; Calculate square of each element, print each & add them together
 ForEach MyList()  
   Print(Str(MyList())+" ")             ; Present to our user
   sum_of_squares+MyList()*MyList()     ; Sum the squares, e.g
 Next

 ;Present the result
 result=Sqr(sum_of_squares/ListSize(MyList()))
 PrintN(#CRLF$+"= "+StrD(result))
 
 PrintN("Press ENTER to exit"): Input()
 CloseConsole()

EndIf</lang>

Python

Works with: Python version 3

<lang Python>>>> from math import sqrt >>> def qmean(num): return sqrt(sum(n*n for n in num)/len(num))

>>> qmean(range(1,11)) 6.2048368229954285</lang> Note that function range in Python includes the first limit of 1, excludes the second limit of 11, and has a default increment of 1.

The Python 2 version of this is nearly identical, except you must cast the sum to a float to get float division instead of integer division; 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.

Alternatively in terms of reduce: <lang python>from functools import (reduce) from math import (sqrt)

rootMeanSquare :: [Num] -> Float

def rootMeanSquare(xs):

   return sqrt(reduce(lambda a, x: a + x * x, xs, 0) / len(xs))

print(

   rootMeanSquare([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])

)</lang>

Output:

6.2048368229954285

Qi

<lang qi>(define rms

 R -> (sqrt (/ (APPLY + (MAPCAR * R R)) (length R))))</lang>

R

We may calculate the answer directly using R's built-in sqrt and mean functions: <lang R>sqrt(mean((1:10)^2))</lang> The following function works for any vector x: <lang R>RMS = function(x){

sqrt(mean(x^2))

}</lang> Usage: <lang R>> RMS(1:10) [1] 6.204837 </lang>

Racket

lang racket

(define (rms nums)

 (sqrt (/ (for/sum ([n nums]) (* n n)) (length nums))))

</lang>

Raku

(formerly Perl 6)

Works with: Rakudo version 2015.12

<lang perl6>sub rms(*@nums) { sqrt [+](@nums X** 2) / @nums }

say rms 1..10;</lang>

Here's a slightly more concise version, albeit arguably less readable: <lang perl6>sub rms { sqrt @_ R/ [+] @_ X** 2 }</lang>

REXX

REXX has no built-in sqrt function, so a RYO version is included here.

This particular sqrt function was programmed for speed, as it has two critical components:

the initial guess (for the square root)
the number of (increasing) decimal digits used during the computations

The sqrt code was optimized to use the minimum amount of digits (precision) for each iteration of the
calculation as well as a reasonable attempt at providing a first-guess square root by essentially halving
the number using logarithmic (base ten) arithmetic. <lang rexx>/*REXX program computes and displays the root mean square (RMS) of a number sequence. */ parse arg nums digs show . /*obtain the optional arguments from CL*/ if nums== | nums=="," then nums=10 /*Not specified? Then use the default.*/ if digs== | digs=="," then digs=50 /* " " " " " " */ if show== | show=="," then show=10 /* " " " " " " */ numeric digits digs /*uses DIGS decimal digits for calc. */ $=0; do j=1 for nums /*process each of the N integers. */

                        $=$ + j**2              /*sum the   squares   of the integers. */
                        end   /*j*/
                                                /* [↓]  displays  SHOW  decimal digits.*/

rms=format( sqrt($/nums), , show ) / 1 /*divide by N, then calculate the SQRT.*/ say 'root mean square for 1──►'nums "is: " rms /*display the root mean square (RMS). */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); numeric digits; m.=9

      numeric form;  parse value format(x,2,1,,0) 'E0'  with  g 'E' _ .;  g=g *.5'e'_ % 2
      h=d+6;    do j=0  while h>9;       m.j=h;                h=h%2+1;        end  /*j*/
                do k=j+5  to 0  by -1;   numeric digits m.k;   g=(g+x/g)*.5;   end  /*k*/
      return g</lang>

output when using the default inputs:

root mean square for 1──►10 is:  6.204836823

Ring

<lang ring> nums = [1,2,3,4,5,6,7,8,9,10] sum = 0 decimals(5) see "Average = " + average(nums) + nl

func average number

    for i = 1 to len(number)
        sum = sum + pow(number[i],2)
    next
    x = sqrt(sum / len(number))
    return x

</lang>

Ruby

<lang ruby>class Array

 def quadratic_mean
   Math.sqrt( self.inject(0.0) {|s, y| s + y*y} / self.length )
 end

end

class Range

 def quadratic_mean
   self.to_a.quadratic_mean
 end

end

(1..10).quadratic_mean # => 6.2048368229954285</lang>

and a non object-oriented solution: <lang ruby>def rms(seq)

 Math.sqrt(seq.sum{|x| x*x}.fdiv(seq.size) )

end puts rms (1..10) # => 6.2048368229954285</lang>

Run BASIC

<lang runbasic>valueList$ = "1 2 3 4 5 6 7 8 9 10" while word$(valueList$,i +1) <> "" ' grab values from list

 thisValue  = val(word$(valueList$,i +1))     ' turn values into numbers
 sumSquares = sumSquares + thisValue ^ 2      ' sum up the squares
 i = i +1                                     '

wend print "List of Values:";valueList$;" containing ";i;" values" print "Root Mean Square =";(sumSquares/i)^0.5</lang>

Output:

List of Values:1 2 3 4 5 6 7 8 9 10 containing 10 values Root Mean Square =6.20483682

Rust

<lang rust>fn root_mean_square(vec: Vec<i32>) -> f32 {

   let sum_squares = vec.iter().fold(0, |acc, &x| acc + x.pow(2));
   return ((sum_squares as f32)/(vec.len() as f32)).sqrt();

}

fn main() {

   let vec = (1..11).collect();
   println!("The root mean square is: {}", root_mean_square(vec));

}</lang>

Output:

The root mean square is: 6.204837

S-lang

Many of math operations in S-Lang are 'vectorized', that is, given an array, they apply themselves to each element. In this case, that means no array_map() function needed. Also, "range arrays" have a built-in syntax.

<lang S-lang>define rms(arr) {

 return sqrt(sum(sqr(arr)) / length(arr));

}

print(rms([1:10]));</lang>

Sather

<lang sather>class MAIN is

 -- irrms stands for Integer Ranged RMS
 irrms(i, f:INT):FLT
   pre i <= f
 is
   sum ::= 0;
   loop
     sum := sum + i.upto!(f).pow(2);
   end;
   return (sum.flt / (f-i+1).flt).sqrt;
 end;

 main is
   #OUT + irrms(1, 10) + "\n";
 end;

end;</lang>

S-BASIC

<lang basic> var n, sqsum, sqmean, rms = real sqsum = 0 for n = 1 to 10 do

 sqsum = sqsum + (n * n)

next n sqmean = sqsum / n rms = sqr(sqmean) print "RMS of numbers from 1 to 10 = ";rms

end </lang>

Output:

RMS of numbers from 1 to 10 =  6.20484

Scala

<lang scala>def rms(nums: Seq[Int]) = math.sqrt(nums.map(math.pow(_, 2)).sum / nums.size) println(rms(1 to 10))</lang>

Output:

6.2048368229954285

Scheme

<lang scheme>(define (rms nums)

 (sqrt (/ (apply + (map * nums nums))
          (length nums))))

(rms '(1 2 3 4 5 6 7 8 9 10))</lang>

Output:

6.20483682299543

Seed7

<lang seed7>$ include "seed7_05.s7i";

 include "float.s7i";
 include "math.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 float: rms (in array float: numbers) is func

 result
   var float: rms is 0.0;
 local
   var float: number is 0.0;
   var float: sum is 0.0;
 begin
   for number range numbers do
     sum +:= number ** 2;
   end for;
   rms := sqrt(sum / flt(length(numbers)));
 end func;

const proc: main is func

 begin
   writeln(rms(numbers) digits 7);
 end func;</lang>

Shen

Works with: shen-scheme version 0.17

<lang Shen>(declare scm.sqrt [number --> number])

(tc +)

(define mean

 { (list number) --> number }
 Xs -> (/ (sum Xs) (length Xs)))

(define square

 { number --> number }
 X -> (* X X))

(define rms

 { (list number) --> number }
 Xs -> (scm.sqrt (mean (map (function square) Xs))))

(define iota-h

 { number --> number --> (list number) }
 X X -> [X]
 X Lim -> (cons X (iota-h (+ X 1) Lim)))

(define iota

 { number --> (list number) }
 Lim -> (iota-h 1 Lim))

(output "~A~%" (rms (iota 10)))</lang>

Sidef

<lang ruby>func rms(a) {

   sqrt(a.map{.**2}.sum / a.len)

}

say rms(1..10)</lang>

Using hyper operators, we can write it as: <lang ruby>func rms(a) { a »**» 2 «+» / a.len -> sqrt }</lang>

Output:

6.20483682299542829806662097772473784992796529536

Smalltalk

<lang smalltalk>(((1 to: 10) inject: 0 into: [ :s :n | n*n + s ]) / 10) sqrt.</lang>

SNOBOL4

Works with: Macro Spitbol

Works with: CSnobol

There is no built-in sqrt( ) function in Snobol4+. <lang SNOBOL4> define('rms(a)i,ssq') :(rms_end) rms i = i + 1; ssq = ssq + (a * a) :s(rms)

rms = sqrt(1.0 * ssq / prototype(a)) :(return)
rms_end
# Fill array, test and display
str = '1 2 3 4 5 6 7 8 9 10'; a = array(10)
loop i = i + 1; str len(p) span('0123456789') . a @p :s(loop)
output = str ' -> ' rms(a)
end</lang>

Output:
1 2 3 4 5 6 7 8 9 10 -> 6.20483682
Standard ML
<lang sml>fun rms(v: real vector) =
let val v' = Vector.map (fn x => x*x) v val sum = Vector.foldl op+ 0.0 v' in Math.sqrt( sum/real(Vector.length(v')) ) end;
rms(Vector.tabulate(10, fn n => real(n+1)));</lang>

Output:
val it = 6.204836823 : real
Stata
Compute the RMS of a variable and return the result in r(rms).
<lang stata>program rms, rclass syntax varname(numeric) [if] [in] tempvar x gen `x'=`varlist'^2 `if' `in' qui sum `x' `if' `in' return scalar rms=sqrt(r(mean)) end</lang>
Example
<lang stata>clear set obs 20 gen x=rnormal()
rms x di r(rms) 1.0394189
rms x if x>0 di r(rms) .7423647</lang>
Swift
<lang swift>extension Collection where Element: FloatingPoint {
@inlinable public func rms() -> Element { return (lazy.map({ $0 * $0 }).reduce(0, +) / Element(count)).squareRoot() }
}
print("RMS of 1...10: \((1...10).map(Double.init).rms())")</lang>

Output:
RMS of 1...10: 6.2048368229954285
Tcl
Works with: Tcl version 8.5
<lang tcl>proc qmean list {
set sum 0.0 foreach value $list { set sum [expr {$sum + $value**2}] } return [expr { sqrt($sum / [llength $list]) }]
}
puts "RMS(1..10) = [qmean {1 2 3 4 5 6 7 8 9 10}]"</lang>

Output:
RMS(1..10) = 6.2048368229954285
Ursala
using the mean function among others from the flo library <lang Ursala>#import nat
import flo
cast %e
rms = sqrt mean sqr* float* nrange(1,10)</lang>

Output:
6.204837e+00
Vala
Valac probably needs to have the flag "-X -lm" added to include the C Math library. <lang vala>double rms(double[] list){ double sum_squares = 0; double mean;
foreach ( double number in list){ sum_squares += (number * number); }
mean = Math.sqrt(sum_squares / (double) list.length);
return mean; } // end rms
public static void main(){ double[] list = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}; double mean = rms(list);
stdout.printf("%s\n", mean.to_string()); }</lang>

Output:
6.2048368229954285
VBA
Using Excel VBA <lang vb>Private Function root_mean_square(s() As Variant) As Double
For i = 1 To UBound(s) s(i) = s(i) ^ 2 Next i root_mean_square = Sqr(WorksheetFunction.sum(s) / UBound(s))
End Function Public Sub pythagorean_means()
Dim s() As Variant s = [{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}] Debug.Print root_mean_square(s)
End Sub</lang> Without using Excel worksheetfunction: <lang vb>Function rms(iLow As Integer, iHigh As Integer)
Dim i As Integer If iLow > iHigh Then i = iLow iLow = iHigh iHigh = i End If For i = iLow To iHigh rms = rms + i ^ 2 Next i rms = Sqr(rms / (iHigh - iLow + 1))
End Function
Sub foo()
Debug.Print rms(1, 10)
End Sub </lang>
Output:
6.20483682299543
Wortel
<lang wortel>@let {
; using a composition and a fork (like you would do in J) rms1 ^(@sqrt @(@sum / #) *^@sq)
; using a function with a named argument rms2 &a @sqrt ~/ #a @sum !*^@sq a
[[ !rms1 @to 10 !rms2 @to 10 ]]
}</lang>

Output:
[6.2048368229954285 6.2048368229954285]
Wren
<lang ecmascript>var rms = ((1..10).reduce(0) { |acc, i| acc + i*i }/10).sqrt System.print(rms)</lang>

Output:
6.2048368229954
XLISP
<lang lisp>(defun quadratic-mean (xs)
(sqrt (/ (apply + (mapcar (lambda (x) (expt x 2)) xs)) (length xs))))
define a RANGE function, for testing purposes
(defun range (x y)
(if (< x y) (cons x (range (+ x 1) y))))
test QUADRATIC-MEAN
(print (quadratic-mean (range 1 11)))</lang>

Output:
6.20483682299543
XPL0
<lang XPL0>code CrLf=9; code real RlOut=48; int N; real S; [S:= 0.0; for N:= 1 to 10 do S:= S + sq(float(N)); RlOut(0, sqrt(S/10.0)); CrLf(0); ]</lang>

Output:
6.20484
Yacas
<lang Yacas>Sqrt(Add((1 .. 10)^2)/10)</lang> The above will give the precise solution ${\sqrt {\frac {77}{2}}}$ , to downgrade to 6.20483682299, surround the expression with 'N()'.
zkl
<lang zkl>fcn rms(z){ ( z.reduce(fcn(p,n){ p + n*n },0.0) /z.len() ).sqrt() }</lang> The order in the reduce function is important as it coerces n*n to float.
zkl: rms([1..10].walk()) //-->rms(T(1,2,3,4,5,6,7,8,9,10)) 6.20484