Averages/Pythagorean means

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

Compute all three of the Pythagorean means of the list of the integers 1 through 10.

• The most common of the three means, the arithmetic mean, is the sum of the list divided by its length:

$A(x_{1},\ldots ,x_{n})={\frac {x_{1}+\cdots +x_{n}}{n}}$

• The geometric mean is the $n$th root of the product of the list:

$G(x_{1},\ldots ,x_{n})={\sqrt[{n}]{x_{1}\cdots x_{n}}}$

• The harmonic mean is $n$ divided by the sum of the reciprocal of each item in the list:

$H(x_{1},\ldots ,x_{n})={\frac {n}{{\frac {1}{x_{1}}}+\cdots +{\frac {1}{x_{n}}}}}$

Haskell

The general function given here yields an arithmetic mean when its first argument is 1, a geometric mean when its first argument is 0, and a harmonic mean when its first argument is -1.

<lang haskell>import Data.List (genericLength) import Control.Monad (zipWithM_)

mean :: Double -> [Double] -> Double mean 0 xs = product xs ** (1 / genericLength xs) mean p xs = (1 / genericLength xs * sum (map (** p) xs)) ** (1/p)

main = zipWithM_ f "agh" (map (flip mean [1 .. 10]) [1, 0, -1])

where f c n = putStrLn $ c : ": " ++ show n</lang>

J

Solution: <lang j>amean=: +/ % # gmean=: # %: */ hmean=: amean&.:%</lang>

Example Usage: <lang j> (amean , gmean , hmean) >: i. 10 5.5 4.528729 3.414172</lang>

Lua

<lang lua>function fsum(f, a, ...) return a and f(a) + fsum(f, ...) or 0 end function pymean(t, f, finv) return finv(fsum(f, unpack(t)) / #t) end nums = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

--arithmetic a = pymean(nums, function(n) return n end, function(n) return n end) --geometric g = pymean(nums, math.log, math.exp) --harmonic h = pymean(nums, function(n) return 1/n end, function(n) return 1/n end) print(a, g, h)</lang>

PL/I

<lang PL/I>declare A(10) float static initial (1,2,3,4,5,6,7,8,9,10); n = hbound(A,1);

/* compute the average */ Average = sum(A)/n;

/* Compute the geometric mean: */ Geometric = prod(A)**(1/n);

/* Compute the Harmonic mean: */ Harmonic = n / sum(1/A);

put skip data (Average); put skip data (Geometric); put skip data (Harmonic);</lang>

Python

Works with: Python 3

<lang Python>from operator import mul from functools import reduce

def amean(num): return sum(num)/len(num)

def gmean(num): return reduce(mul, num, 1)**(1/len(num))

def hmean(num): return len(num)/sum(1/n for n in num)

numbers = range(1,11) # 1..10 print(amean(numbers), gmean(numbers), hmean(numbers))</lang>

Output:

5.5 4.52872868812 3.41417152147

Tcl

<lang tcl>proc arithmeticMean list {

   set sum 0.0
   foreach value $list { set sum [expr {$sum + $value}] }
   return [expr {$sum / [llength $list]}]

} proc geometricMean list {

   set product 1.0
   foreach value $list { set product [expr {$product * $value}] }
   return [expr {$product ** (1.0/[llength $list])}]

} proc harmonicMean list {

   set sum 0.0
   foreach value $list { set sum [expr {$sum + 1.0/$value}] }
   return [expr {[llength $list] / $sum}]

}

set nums {1 2 3 4 5 6 7 8 9 10} set A10 [arithmeticMean $nums] set G10 [geometricMean $nums] set H10 [harmonicMean $nums] puts "A10=$A10, G10=$G10, H10=$H10"</lang> Output:

A10=5.5, G10=4.528728688116765, H10=3.414171521474055