Averages/Root mean square

Averages/Root mean square
You are encouraged to solve this task according to the task description, using any language you may know.

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

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

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

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

C.f. Averages/Pythagorean means

Haskell

Given the mean function defiend in Averages/Pythagorean means:

<lang haskell>main = print $ mean 2 [1 .. 10]</lang>

J

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

Example Usage: <lang j> rms >: i. 10 6.20484</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>

PL/I

<lang PL/I> declare A(10) fixed decimal static initial (1,2,3,4,5,6,7,8,9,10); n = hbound(A,1); RMS = sqrt(sum(A**2)/n); </lang>

Python

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

>>> numbers = range(1,11) # 1..10 >>> qmean(numbers) 6.2048368229954285</lang>

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