Step by Step solution about How to resolve the algorithm Averages/Root mean square step by step in the Ruby programming language

The provided Ruby code defines two methods, quadratic_mean and rms, to calculate the quadratic mean (root mean square) of a given sequence. Here's what the code does:

1. quadratic_mean method for Array:

   • This method extends the Array class to calculate the quadratic mean of its elements.
   • The quadratic mean is essentially the square root of the average of squared values.
   • The method uses the inject method to sum up the squares of each element and then divides it by the length of the array.
   • Finally, it takes the square root of the result to obtain the quadratic mean.

2. quadratic_mean method for Range:

   • This method extends the Range class to calculate the quadratic mean of the range's values.
   • It converts the range to an array using the to_a method and then calls the quadratic_mean method for arrays to compute the quadratic mean.

3. rms method:

   • The rms method is a custom method that calculates the root mean square (quadratic mean) of a given sequence.
   • It takes a sequence (e.g., an array or range) as an argument.
   • It uses the sum method to calculate the sum of the squared values of the elements in the sequence.
   • Then, it divides the sum by the size of the sequence to get the average.
   • Finally, it takes the square root of the average to obtain the root mean square.

4. Usage:

   • The code demonstrates the usage of these methods to calculate the quadratic mean of a range and a sequence.
   • It calculates the quadratic mean of the range (1..10) using the quadratic_mean method and prints the result.
   • It also calculates the root mean square of the range (1..10) using the rms method and prints the result.

In summary, this code provides two methods, quadratic_mean for arrays and ranges, and rms for calculating the quadratic mean of any sequence. The methods calculate the square root of the average of squared values, which is useful for statistical calculations in various applications.

class Array
  def quadratic_mean
    Math.sqrt( self.inject(0.0) {|s, y| s + y*y} / self.length )
  end
end

class Range
  def quadratic_mean
    self.to_a.quadratic_mean
  end
end

(1..10).quadratic_mean  # => 6.2048368229954285


def rms(seq)
  Math.sqrt(seq.sum{|x| x*x}.fdiv(seq.size) )
end
puts rms (1..10)   # => 6.2048368229954285