new_contents: import numpy as np
  from scipy import stats
  
  def hotelling_1d(data, threshold):
      """
      Parameters
          ----------
          data : Numpy array
          threshold : float
  
      Returns
      -------
          List of tuples where each tuple contains index number and anomalous value.
      """
      #Set the threshold of abnormality
      abn_th = stats.chi2.interval(1-threshold, 1)[1]
  
      #Covert raw data into the degree of abnormality
      avg = np.average(data)
      var = np.var(data)
      data_abn = [(x - avg)**2 / var for x in data]
  
      #Abnormality determination
      result = []
      for (index, x) in enumerate(data_abn):
          if x > abn_th:
              result.append((index, data[index]))
      return result
  
subject: Add module of outlier detection based on hotelling theory