input: Write a function to calculate the Gini coefficient of a given dataset.
  def gini(x):
      """Calculate Gini Coefficient of a given dataset."""
      # calculate the frequency of each item in x
      x_value_counts = x.value_counts().sort_index() 
  
      # calculate the cumulative sum of x_value_counts
      x_cum_sum = x_value_counts.cumsum()
  
      # calculate the Lorenz values
      n = len(x)
      lorenz = x_cum_sum / n
      lorenz = np.insert(lorenz, 0, 0) # add 0 to the beginning of array
  
      # calculate the Gini Coefficient
      width = lorenz[:-1] - lorenz[1:]
      gini_coef = (1 / n) * sum(width * (lorenz[1:] + lorenz[:-1]))
  
      return gini_coef
  
  if __name__ == '__main__':
      x = np.array([2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,21])
      gini_coef = gini(x)
      print(gini_coef) # should print 0.605
  assert gini(np.array([2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,21])) == 0.605
  assert gini(np.array([1,2,3,4,5,6,7,8,9,10])) == 0.3
  assert gini(np.array([1,1,1,1,1,1,1,1,1])) == 0.0
  assert gini(np.array([1,2,1,2,1,2,1,2,1,2])) == 0.36
output: def gini(x):
      x_value_counts = x.value_counts().sort_index()
      x_cum_sum = x_value_counts.cumsum()
      n = len(x)
      lorenz = x_cum_sum / n
      lorenz = np.insert(lorenz, 0, 0)
      width = lorenz[:-1] - lorenz[1:]
      gini_coef = (1 / n) * sum(width * (lorenz[1:] + lorenz[:-1]))
      return gini_coef