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Compute the [[wp:Root mean square|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:

::: $x_\left\{\mathrm\left\{rms\right\}\right\} = \sqrt \left\{\left\{\left\{x_1\right\}^2 + \left\{x_2\right\}^2 + \cdots + \left\{x_n\right\}^2\right\} \over n\right\}.$

## 11l

{{trans|Python}}

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

print(qmean(1..10))


{{out}}


6.20484



with Ada.Float_Text_IO; use Ada.Float_Text_IO;
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;


{{out}}


6.20484



## ALGOL 68

{{works with|ALGOL 68|Standard - no extensions to language used}} {{works with|ALGOL 68G|Any - tested with release [http://sourceforge.net/projects/algol68/files/algol68g/algol68g-1.18.0/algol68g-1.18.0-9h.tiny.el5.centos.fc11.i386.rpm/download 1.18.0-9h.tiny]}} {{works with|ELLA ALGOL 68|Any (with appropriate job cards)}}

# 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))
)


{{out}}


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



## ALGOL W

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.


{{out}}


rms of 1 .. 10:     6.2048



## APL

 rms←{((+/⍵*2)÷⍴⍵)*0.5}
x←⍳10

rms x
6.204836823


## AppleScript

{{Trans|JavaScript}}( ES6 version )

-- 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


{{Out}}

6.204836822995


## Astro

sqrt(mean(x²))


## AutoHotkey

### Using a loop

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)
}


Message box shows:


6.204837



### Avoiding a loop

Using these equations:

$\sum_\left\{i=1\right\}^n i^2 = \frac\left\{n\left(n+1\right)\left(2n+1\right)\right\}\left\{6\right\}$ See [[wp:List of mathematical series]]

for $a : $\sum_\left\{i=a\right\}^b i^2 = \sum_\left\{i=1\right\}^b i^2 - \sum_\left\{i=1\right\}^\left\{a-1\right\} i^2$

We can show that:

$\sum_\left\{i=a\right\}^b i^2 = \frac\left\{b\left(b+1\right)\left(2b+1\right)-a\left(a-1\right)\left(2a-1\right)\right\}\left\{6\right\}$

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))
}


Message box shows:


6.204837



## AWK

#!/usr/bin/awk -f
# computes RMS of the 1st column of a data file
{
x  = $1; # value of 1st column S += x*x; N++; } END { print "RMS: ",sqrt(S/N); }  ## BASIC {{works with|QBasic}} Note that this will work in [[Visual Basic]] and the Windows versions of [[PowerBASIC]] by simply wrapping the module-level code into the MAIN function, and changing PRINT to MSGBOX. DIM i(1 TO 10) AS DOUBLE, L0 AS LONG FOR L0 = 1 TO 10 i(L0) = L0 NEXT PRINT STR$(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


See also: [[#BBC BASIC|BBC BASIC]], [[#Liberty BASIC|Liberty BASIC]], [[#PureBasic|PureBasic]], [[#Run BASIC|Run BASIC]]

=

## Applesoft BASIC

=

 10 N = 10
20  FOR I = 1 TO N
30 S = S + I * I
40  NEXT
50 X =  SQR (S / N)
60  PRINT X


{{out}}

6.20483683


==={{header|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



=
## Sinclair ZX81 BASIC
=

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


{{out}}

6.2048368


=

## BBC BASIC

=

      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)


## 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;
}


## C#

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);
}
}
}


An alternative method demonstrating the more functional style introduced by LINQ and lambda expressions in C# 3. {{works with|C sharp|C#|3}}

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));
}
}
}


## C++

#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 ;
}


{{out}}


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



## Clojure


(defn rms [xs]
(Math/sqrt (/ (reduce + (map #(* % %) xs))
(count xs))))

(println (rms (range 1 11)))


{{out}}


6.2048368229954285



## COBOL

Could be written more succinctly, with an inline loop and more COMPUTE statements; but that wouldn't be very COBOLic.

IDENTIFICATION DIVISION.
DATA DIVISION.
WORKING-STORAGE SECTION.
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.


{{out}}

6.204836822995428


## CoffeeScript

{{trans|JavaScript}}

    root_mean_square = (ary) ->
sum_of_squares = ary.reduce ((s,x) -> s + x*x), 0
return Math.sqrt(sum_of_squares / ary.length)



## Common 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))))


Here's a non-iterative solution.


(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))



## Crystal

{{trans|Ruby}}

def rms(seq)
Math.sqrt(seq.reduce(0.0) {|sum, x| sum + x*x} / seq.size)
end

puts rms (1..10).to_a



{{out}}


6.2048368229954285



## 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);
}


{{out}}


6.2048368229954282979



program AveragesMeanSquare;

}
}


## Factor

: root-mean-square ( seq -- mean )
[ [ sq ] map-sum ] [ length ] bi / sqrt ;


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

## 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


## Fortran

Assume $x$ stored in array x.

print *,sqrt( sum(x**2)/size(x) )


## 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
Next

Print "Quadratic mean (or RMS) is :"; QuadraticMean(vector())
Print
Print "Press any key to quit the program"
Sleep



{{out}}


Quadratic mean (or RMS) is : 6.204836822995429



## Futhark


import "futlib/math"

fun main(as: [n]f64): f64 =
f64.sqrt ((reduce (+) 0.0 (map (**2.0) as)) / f64(n))



## GEORGE


1, 10 rep (i)
i i | (v) ;
0
1, 10 rep (i)
i dup mult +
]
10 div
sqrt
print



6.204836822995428



## 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))
}


{{out}}


6.2048368229954285



## Groovy

Solution:

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


Test:

def list = 1..10
def Q = quadMean(list)
println """
list: ${list} Q:${Q}
"""


{{out}}

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


Given the mean function defined in [[Averages/Pythagorean means]]:

main = print $mean 2 [1 .. 10]  Or, writing a naive '''mean''' of our own, (but see https://donsbot.wordpress.com/2008/06/04/haskell-as-fast-as-c-working-at-a-high-altitude-for-low-level-performance/): import Data.List (genericLength) rootMeanSquare :: [Double] -> Double rootMeanSquare = sqrt . (((/) . foldr ((+) . (^ 2)) 0) <*> genericLength) main :: IO () main = print$ rootMeanSquare [1 .. 10]


{{Out}}

6.2048368229954285


## HicEst

sum = 0
DO i = 1, 10
sum = sum + i^2
ENDDO
WRITE(ClipBoard) "RMS(1..10) = ", (sum/10)^0.5


RMS(1..10) = 6.204836823

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

procedure qmean(L[])             #: quadratic mean
local m
if *L = 0 then fail
every (m := 0.0) +:= !L^2
return sqrt(m / *L)
end


## Io

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

rms( Range 1 to(10) asList ) println


## J

'''Solution:'''

rms=: (+/ % #)&.:*:


'''Example Usage:'''

  rms 1 + i. 10
6.20484


*: means [http://jsoftware.com/help/dictionary/d112.htm square]

(+/ % #) is an idiom for [[../Arithmetic_mean#J|mean]].

&.: means [http://jsoftware.com/help/dictionary/d631c.htm 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 [http://jsoftware.com/help/dictionary/d631.htm &.] which does basically the same thing but with different granularity -- item at a time instead of everything at once.

## 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));
}
}


{{out}}

The RMS of the numbers from 1 to 10 is 6.2048368229954285


## JavaScript

### ES5

{{works with|JavaScript|1.8}} {{works with|Firefox|3.0}}

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


### ES6

(() => {
'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
})();


{{Out}}

6.2048368229954285


## jq

The following filter returns ''null'' if given an empty array:

def rms: length as $length | if$length == 0 then null
else map(. * .) | add | sqrt / $length end ;  With this definition, the following program would compute the rms of each array in a file or stream of numeric arrays:  ## Julia There are a variety of ways to do this via built-in functions in Julia, given an array <code>A = [1:10]</code> of values. The formula can be implemented directly as: julia sqrt(sum(A.^2.) / length(A))  or shorter with using Statistics (and as spoken: root-mean-square) sqrt(mean(A.^2.))  or the implicit allocation of a new array by A.^2. can be avoided by using sum as a higher-order function: sqrt(sum(x -> x*x, A) / length(A))  One can also use an explicit loop for near-C performance  function rms(A) s = 0.0 for a in A s += a*a end return sqrt(s / length(A)) end  Potentially even better is to use the built-in norm function, which computes the square root of the sum of the squares of the entries of A in a way that avoids the possibility of spurious floating-point overflow (if the entries of A are so large that they may overflow if squared): norm(A) / sqrt(length(A))  ## K  rms:{_sqrt (+/x^2)%#x} rms 1+!10 6.204837  ## Kotlin // version 1.0.5-2 fun quadraticMean(vector: Array<Double>) : Double { val sum = vector.sumByDouble { it * it } return Math.sqrt(sum / vector.size) } fun main(args: Array<String>) { val vector = Array(10, { (it + 1).toDouble() }) print("Quadratic mean of numbers 1 to 10 is${quadraticMean(vector)}")
}


{{out}}


Quadratic mean of numbers 1 to 10 is 6.2048368229954285



## Lasso

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


{{out}}

6.204837


## Liberty BASIC

'   [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

}
}


## 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



{{out}}


RMS of values from 1 to 10: 6.204836822995428



## 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])


{{out}}

6.2048368229954285e+00



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;
END QM.



{{out}}





## 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();
}
}
}


## 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 *)


## Oforth

10 seq map(#sq) sum 10.0 / sqrt .


{{out}}


6.20483682299543



## 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


{{out}}

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

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}}}


{{out}}


6.2048



## PARI/GP

General RMS calculation:

RMS(v)={
sqrt(sum(i=1,#v,v[i]^2)/#v)
};

RMS(vector(10,i,i))


Specific functions for the first ''n'' positive integers:

RMS_first(n)={
sqrt((n+1)*(2*n+1)/6)
};

RMS_first(10)


Asymptotically this is n/sqrt(3).

## Perl

use v5.10.0;
sub rms
{
my $r = 0;$r += $_**2 for @_; sqrt($r/@_ );
}

say rms(1..10);


## Perl 6

{{works with|Rakudo|2015.12}}

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

say rms 1..10;


Here's a slightly more concise version, albeit arguably less readable:

sub rms { sqrt @_ R/ [+] @_ X** 2 }


## 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})


{{out}}


6.204836823



## 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));



{{out}}


6.2048368229954



## 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 ) ) )


{{out}}

6.20484


## 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;


{{out}}

RMS= 6.20483682299543E+0000;


## 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


{{out}}


6.20483685



[1 10] 1 range dup 0 {dup * +} fold exch length div sqrt


## 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


function get-rms([float[]]$nums){$sqsum=$nums | foreach-object {$_*$_} | measure-object -sum | select-object -expand Sum return [math]::sqrt($sqsum/$nums.count) } get-rms @(1..10)  ## PureBasic NewList MyList() ; To hold a unknown amount of numbers to calculate If OpenConsole() Define.d result Define i, sum_of_squares ;Populate a random amounts of numbers to calculate For i=0 To (Random(45)+5) ; max elements is unknown to the program AddElement(MyList()) MyList()=Random(15) ; Put in a random number Next Print("Averages/Root mean square"+#CRLF$+"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  ## Python {{works with|Python|3}}  from math import sqrt >>> def qmean(num): return sqrt(sum(n*n for n in num)/len(num)) >>> qmean(range(1,11)) 6.2048368229954285  Note that function [http://docs.python.org/release/3.2/library/functions.html#range 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''': 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]) )  {{Out}} 6.2048368229954285  ## Qi (define rms R -> (sqrt (/ (APPLY + (MAPCAR * R R)) (length R))))  ## R We may calculate the answer directly using R's built-in sqrt and mean functions: sqrt(mean((1:10)^2))  The following function works for any vector x: RMS = function(x){ sqrt(mean(x^2)) }  Usage:  RMS(1:10) [1] 6.204837  ## Racket  #lang racket (define (rms nums) (sqrt (/ (for/sum ([n nums]) (* n n)) (length nums))))  ## 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. /*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($/nums), , show ) / 1 /*divide by N, then calculate the SQRT.*/ say 'root mean square for 1──►'nums "is: " rms /*display the root mean square (RMS). */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); numeric digits; m.=9 numeric form; parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g *.5'e'_ % 2 h=d+6; do j=0 while h>9; m.j=h; h=h%2+1; end /*j*/ do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/ return g  '''output''' when using the default inputs:  root mean square for 1──►10 is: 6.204836823  ## Ring  nums = [1,2,3,4,5,6,7,8,9,10] sum = 0 decimals(5) see "Average = " + average(nums) + nl func average number for i = 1 to len(number) sum = sum + pow(number[i],2) next x = sqrt(sum / len(number)) return x  ## Ruby class Array def quadratic_mean Math.sqrt( self.inject(0.0) {|s, y| s + y*y} / self.length ) end end class Range def quadratic_mean self.to_a.quadratic_mean end end (1..10).quadratic_mean # => 6.2048368229954285  and a non object-oriented solution: def rms(seq) Math.sqrt(seq.inject(0.0) {|sum, x| sum + x*x} / seq.length) end puts rms (1..10).to_a # => 6.2048368229954285  ## Run BASIC valueList$   = "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  {{out}} List of Values:1 2 3 4 5 6 7 8 9 10 containing 10 values Root Mean Square =6.20483682 ## 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)); }  {{out}} The root mean square is: 6.204837 =={{header|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. define rms(arr) { return sqrt(sum(sqr(arr)) / length(arr)); } print(rms([1:10]));  ## Sather 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;  ## Scala def rms(nums: Seq[Int]) = math.sqrt(nums.map(math.pow(_, 2)).sum / nums.size) println(rms(1 to 10))  {{out}} 6.2048368229954285  ## Scheme (define (rms nums) (sqrt (/ (apply + (map * nums nums)) (length nums)))) (rms '(1 2 3 4 5 6 7 8 9 10))  {{out}} 6.20483682299543  ## 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;


## Shen

{{works with|shen-scheme|0.17}}

(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)))


## Sidef

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

say rms(1..10)


Using hyper operators, we can write it as:

func rms(a) { a »**» 2 «+» / a.len -> sqrt }


{{out}}

6.20483682299542829806662097772473784992796529536


## Smalltalk

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


## SNOBOL4

{{works with|Macro Spitbol}} {{works with|CSnobol}} There is no built-in sqrt( ) function in Snobol4+.

        define('rms(a)i,ssq') :(rms_end)
rms     i = i + 1; ssq = ssq + (a<i> * a<i>) :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<i> @p :s(loop)
output = str ' -> ' rms(a)
end


{{out}}

1 2 3 4 5 6 7 8 9 10 -> 6.20483682


## Standard ML

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)));


{{out}}

val it = 6.204836823 : real


## Stata

Compute the RMS of a variable and return the result in r(rms).

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


'''Example'''

clear
set obs 20
gen x=rnormal()

rms x
di r(rms)
1.0394189

rms x if x>0
di r(rms)
.7423647


## Tcl

{{works with|Tcl|8.5}}

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}]"


{{out}}


RMS(1..10) = 6.2048368229954285



## Ursala

using the mean function among others from the flo library

#import nat
#import flo

#cast %e

rms = sqrt mean sqr* float* nrange(1,10)


{{out}}


6.204837e+00



## Vala

Valac probably needs to have the flag "-X -lm" added to include the C Math library.

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());
}


{{out}}


6.2048368229954285



## VBA

Using Excel VBA

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


Without using Excel worksheetfunction:

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



Output:


6.20483682299543



## 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
]]
}


{{out}}

[6.2048368229954285 6.2048368229954285]


## XLISP

(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))))

(print (quadratic-mean (range 1 11)))


{{out}}

6.20483682299543


## 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);
]


{{out}}


6.20484



## Yacas

Sqrt(Add((1 .. 10)^2)/10)


The above will give the precise solution $\sqrt\left\{\frac\left\{77\right\}\left\{2\right\}\right\}$, to downgrade to 6.20483682299, surround the expression with 'N()'.

## zkl

fcn rms(z){ ( z.reduce(fcn(p,n){ p + n*n },0.0) /z.len() ).sqrt() }


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

`