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

This Python code calculates the arithmetic mean (amean), geometric mean (gmean), and harmonic mean (hmean) of a given range of numbers. It utilizes the built-in functions sum() and reduce() and the operator.mul function for multiplication. The code also defines a list of numbers and calculates the mean values for this list.

1. Arithmetic Mean (amean):
   • The amean function calculates the arithmetic mean of a list of numbers.
   • It uses the sum() function to add all the numbers and divides the result by the number of elements in the list using the len() function.
   • It returns the arithmetic mean as a floating-point number.

def amean(num):
   return sum(num) / len(num)

2. Geometric Mean (gmean):
   • The gmean function calculates the geometric mean of a list of numbers.
   • It uses the reduce() function from the functools module to multiply all the numbers together and then raise the result to the power of 1 divided by the number of elements in the list.
   • This operation effectively calculates the nth root of the product of all the numbers.

def gmean(num):
   return reduce(mul, num, 1)**(1 / len(num))

3. Harmonic Mean (hmean):
   • The hmean function calculates the harmonic mean of a list of numbers.
   • It does this by summing the reciprocals of each number (1/n) and then dividing the number of elements by the sum of the reciprocals.

def hmean(num):
   return len(num) / sum(1 / n for n in num)

4. Usage:
   • The code defines a list of numbers numbers ranging from 1 to 10.
   • It calculates the arithmetic mean (a), geometric mean (g), and harmonic mean (h) for this list.
   • The calculated mean values are printed using the print() function.
   • The code also includes an assertion (assert a >= g >= h) to check if 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 assertion is true for most lists of positive numbers, indicating that the calculated means are consistent with expected mathematical relationships.

from operator import mul
from functools import reduce


def amean(num):
    return sum(num) / len(num)


def gmean(num):
    return reduce(mul, num, 1)**(1 / len(num))


def hmean(num):
    return len(num) / sum(1 / n for n in num)


numbers = range(1, 11)  # 1..10
a, g, h = amean(numbers), gmean(numbers), hmean(numbers)
print(a, g, h)
assert a >= g >= h