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Robust Z-Score Method

Also known as the Median Absolute Deviation method, it is similar to Z-score method with some changes in parameters. Since mean and standard deviations are heavily influenced by outliers, instead of them we will be using median and absolute deviation from median.

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Suppose x follows a standard normal distribution. The MAD will converge to the median of the half normal distribution, which is the 75% percentile of a normal distribution, and N(0.75) is approximately equal to 0.6745.

INSTRUCTIONS
  • First we will import Numpy as np and scipy.stats as stats

    import numpy as <<your code goes here>>
    import scipy.stats as <<your code goes here>>
    
  • Next, we will use the same datapoints we used previously

    x = [5, 5, 5, -99, 5, 5, 5, 5, 5, 5, 88, 5, 5, 5]
    
  • Now, we will define a function calculate_rzscore that will detect the outliers using the robust z-score method

    def <<your code goes here>>(data):
        out=[]
        med = np.median(data) 
        ma = stats.median_absolute_deviation(data)
        for i in data: 
            z = (0.6745*(i-med))/ (np.median(ma))
            if np.abs(z) > 3: 
                out.append(i)
        print("Outliers:",out)
    
  • Finally, we will call the function using our datapoints

    calculate_rzscore(<<your code goes here>>)
    

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