Step by Step solution about How to resolve the algorithm Averages/Pythagorean means step by step in the C# programming language

Program Overview: This C# program demonstrates how to calculate the arithmetic mean (average), geometric mean, and harmonic mean of a sequence of numbers. Explanation: 1. Data Initialization:

• The program starts by creating an enumerable sequence of integers from 1 to 10 using LINQ. This sequence is stored in the nums variable. 2. Mean Calculations:
• The program calculates three types of means:
  • Average() calculates the arithmetic mean or average of the numbers in the nums sequence.
  • Gmean() calculates the geometric mean, which is the nth root of the product of all numbers in the sequence.
  • Hmean() calculates the harmonic mean, which is the reciprocal of the arithmetic mean of the reciprocals of the numbers in the sequence. 3. Output:
• The program prints the calculated means to the console. 4. Assertion:
• The program uses a Debug.Assert check to verify that the arithmetic mean is greater than or equal to the geometric mean, which in turn is greater than or equal to the harmonic mean. This is a mathematical property of means. 5. Extension Methods:
• The Gmean and Hmean methods are defined as extension methods for the IEnumerable<double> type. This allows them to be called directly on the nums sequence. 6. Implementation of Extension Methods:
• The Gmean method uses Aggregate to multiply all the numbers in the sequence and then takes the nth root of it (where n is the count of numbers).
• The Hmean method calculates the sum of the reciprocals of the numbers and then divides the count of numbers by this sum. 7. Main Function:
• The Main function is the entry point of the program. It initializes the nums sequence, calculates the means, and displays the results.

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;

namespace PythMean
{
    static class Program
    {
        static void Main(string[] args) {
            var nums = from n in Enumerable.Range(1, 10) select (double)n;

            var a = nums.Average();
            var g = nums.Gmean();
            var h = nums.Hmean();

            Console.WriteLine("Arithmetic mean {0}", a);
            Console.WriteLine("Geometric mean  {0}", g);
            Console.WriteLine("Harmonic mean   {0}", h);

            Debug.Assert(a >= g && g >= h);
        }

        // Geometric mean extension method.
        static double Gmean(this IEnumerable<double> n) {
            return Math.Pow(n.Aggregate((s, i) => s * i), 1.0 / n.Count());
        }

        // Harmonic mean extension method.
        static double Hmean(this IEnumerable<double> n) {
            return n.Count() / n.Sum(i => 1.0 / i);
        }
    }
}