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






import math
 
fn main() {
    mut sum := 0.0
    mut prod :=1.0
    mut recip_sum := 0.0
    n := 10
 
    for val in 1..(n + 1) {
        sum += val
        prod *= val
        recip_sum = recip_sum + ( 1.0 / val )
    }
 
    a := sum / n
    g := math.pow( prod, ( 1.0 / f32(n) ) )
    h := n / recip_sum
 
    result := 'Arithmetic Mean: ${a:3.2f} \nGeometric Mean: ${g:3.2f}\nHarmonic Mean: ${h:3.2f}'
    println( result )
 
    compare := if a >= g && g >= h { "Yes" } else { "Nope" } 
    println('Is A >= G >= H? $compare')
}