Task[edit]
Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive).

Show that 



A
(

x

1


,
…
,

x

n


)
≥
G
(

x

1


,
…
,

x

n


)
≥
H
(

x

1


,
…
,

x

n


)


{\displaystyle A(x_{1},\ldots ,x_{n})\geq G(x_{1},\ldots ,x_{n})\geq H(x_{1},\ldots ,x_{n})}

 for this set of positive integers.

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



A
(

x

1


,
…
,

x

n


)
=




x

1


+
⋯
+

x

n



n




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


 The geometric mean is the 



n


{\displaystyle n}

th root of the product of the list:
 



G
(

x

1


,
…
,

x

n


)
=




x

1


⋯

x

n




n





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


 The harmonic mean is 



n


{\displaystyle n}

 divided by the sum of the reciprocal of each item in the list:
 



H
(

x

1


,
…
,

x

n


)
=


n



1

x

1




+
⋯
+


1

x

n









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




See also
Tasks for calculating statistical measures



in one go
moving (sliding window)
moving (cumulative)

Mean
Arithmetic

Statistics/Basic
Averages/Arithmetic mean
Averages/Pythagorean means


Averages/Simple moving average




Geometric

Averages/Pythagorean means




Harmonic

Averages/Pythagorean means




Quadratic

Averages/Root mean square




Circular

Averages/Mean angle
Averages/Mean time of day




Median

Averages/Median




Mode

Averages/Mode




Standard deviation

Statistics/Basic



Cumulative standard deviation






%% Author: Abhay Jain <abhay_1303@yahoo.co.in>
 
-module(mean_calculator).
-export([find_mean/0]).
 
find_mean() ->
%% This is function calling. First argument is the the beginning number
%% and second argument is the initial value of sum for AM & HM and initial value of product for GM.
	arithmetic_mean(1, 0),
	geometric_mean(1, 1),
	harmonic_mean(1, 0).
 
%% Function to calculate Arithmetic Mean
arithmetic_mean(Number, Sum) when Number > 10 ->
	AM = Sum / 10,
	io:format("Arithmetic Mean ~p~n", [AM]);
arithmetic_mean(Number, Sum) ->
	NewSum = Sum + Number,
	arithmetic_mean(Number+1, NewSum).
 
%% Function to calculate Geometric Mean
geometric_mean(Number, Product) when Number > 10 ->
	GM = math:pow(Product, 0.1),
	io:format("Geometric Mean ~p~n", [GM]);
geometric_mean(Number, Product) ->
	NewProd = Product * Number,
	geometric_mean(Number+1, NewProd).
 
%% Function to calculate Harmonic Mean
harmonic_mean(Number, Sum) when Number > 10 ->
	HM = 10 / Sum,
	io:format("Harmonic Mean ~p~n", [HM]);
harmonic_mean(Number, Sum) ->
	NewSum = Sum + (1/Number),
	harmonic_mean(Number+1, NewSum). 