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

The provided Ruby code defines two different methods named median to calculate the median of an array of numbers.

Method 1: The first method, median(ary), takes an array ary as input and calculates the median as follows:

1. It checks if the array is empty. If it is, it returns nil.
2. It calculates the middle index mid and the remainder rem of dividing the array's length by 2.
3. If the remainder is 0 (even-length array), it sorts the array and takes the average of the two middle elements.
4. If the remainder is not 0 (odd-length array), it sorts the array and returns the middle element as the median.

Method 2: The second method, also named median(aray), is a modified version of the first method with a slightly different approach:

1. It first sorts the input array aray in ascending order.
2. It calculates the length of the sorted array alen.
3. It uses the formula (srtd[(alen-1)/2] + srtd[alen/2]) / 2.0 to calculate the median. This formula essentially finds the average of the middle two elements (for even-length arrays) or the middle element (for odd-length arrays).

Usage Examples: The provided code includes several usage examples to demonstrate how the median methods work with different input arrays:

1. p median([]) returns nil because an empty array has no median.
2. p median([5,3,4]) returns 4, which is the median of the array.
3. p median([5,4,2,3]) returns 3.5, which is the average of the two middle elements when the array is sorted.
4. p median([3,4,1,-8.4,7.2,4,1,1.2]) returns 2.1, which is the median of the sorted array.

def median(ary)
  return nil if ary.empty?
  mid, rem = ary.length.divmod(2)
  if rem == 0
    ary.sort[mid-1,2].inject(:+) / 2.0
  else
    ary.sort[mid]
  end
end

p median([])                        # => nil
p median([5,3,4])                   # => 4
p median([5,4,2,3])                 # => 3.5
p median([3,4,1,-8.4,7.2,4,1,1.2])  # => 2.1


def median(aray)
    srtd = aray.sort
    alen = srtd.length
    (srtd[(alen-1)/2] + srtd[alen/2]) / 2.0
end