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
*n*th root of the product of the list:

- 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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