Compute all three of the Pythagorean means of the set of integers 1 through 10.
Show that 
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:
- The geometric mean is the nth root of the product of the list:
![G(x_1, \ldots, x_n) = \sqrt[n]{x_1 \cdots x_n}](https://i0.wp.com/rosettacode.org/mw/images/math/1/2/5/12595bb2b15b5d8b7263aba68c137db3.png?w=640)
- The harmonic mean is n divided by the sum of the reciprocal of each item in the list:
#include <vector> #include <iostream> #include <numeric> #include <cmath> #include <algorithm> double toInverse ( int i ) { return 1.0 / i ; } int main( ) { std::vector<int> numbers ; for ( int i = 1 ; i < 11 ; i++ ) numbers.push_back( i ) ; double arithmetic_mean = std::accumulate( numbers.begin( ) , numbers.end( ) , 0 ) / 10.0 ; double geometric_mean = pow( std::accumulate( numbers.begin( ) , numbers.end( ) , 1 , std::multiplies<int>( ) ), 0.1 ) ; std::vector<double> inverses ; inverses.resize( numbers.size( ) ) ; std::transform( numbers.begin( ) , numbers.end( ) , inverses.begin( ) , toInverse ) ; double harmonic_mean = 10 / std::accumulate( inverses.begin( ) , inverses.end( ) , 0.0 ); //initial value of accumulate must be a double! std::cout << "The arithmetic mean is " << arithmetic_mean << " , the geometric mean " << geometric_mean << " and the harmonic mean " << harmonic_mean << " !\n" ; return 0 ; }
- Output:
The arithmetic mean is 5.5 , the geometric mean 4.52873 and the harmonic mean 3.41417 !
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