Variable evaluation | set 1

NumPy | Python Methods and Functions

Terms related to variability metrics:

 - & gt; Deviation - & gt; Variance - & gt; Standard Deviation - & gt; Mean Absolute Deviation - & gt; Meadian Absolute Deviation - & gt; Order Statistics - & gt; Range - & gt; Percentile - & gt; Inter-quartile Range 
  • Deviation: we can call it — errors or leftovers too. It is a measure of how different / scattered the values ​​are from the central / observed value. 
    Example:
     Sequence: [2, 3, 5, 6, 7, 9] Suppose, Central / Observed Value = 7 Deviation = [-5, -4, -2 , -1, 0, 2] 
  • Variance (with 2 ): This is the most famous measure for assessing variability because it represents is the squared deviation. This can be called the root mean square error, because it is the mean of the standard deviation. 

    Example:

     Sequence: [2, 3, 5, 6, 7, 9] Mean = 5.33 Total Terms, n = 6 Squared Deviation = (2 - 5.33)  2  + (3 - 5.33)  2  + (5 - 5.33)  2  (6 - 5.33)  2  + (7 - 5.33)  2  + (9 - 5.33)  2  Variance = Squared Deviation / n 

    Code —

    # Dispersion

      

    import numpy as np

     

    Sequence = [ 2 , 3 , 5 , 6 , 7 , 9 ]

     

    var = np.var (Sequence)

     

    print ( "Variance:" , var)

    Output:

     Variance: 5.5555555555555545 
  • Standard Deviation: is the square root of the variance. Also referred to as Euclidean norm

    Example:

     Sequence: [2, 3, 5, 6, 7, 9] Mean = 5.33 Total Terms, n = 6 Squared Deviation = (2 - 5.33)  2  + (3 - 5.33)  2  + (5 - 5.33)  2  (6 - 5.33)  2  + (7 - 5.33)  2  + (9 - 5.33)  2  Variance = Squared Deviation / n Standard Deviation = (Variance)  1/2  

    Code —

    # Standard deviation

     

    import numpy as np

     

    Sequence = [ 2 , 3 , 5 , 6 , 7 , 9 ]

     

    std = np.std (Sequence)

     

    print ( "Standard Deviation:" , std)

    Output:

     Standard Deviation: 2.357022603955158 
  • Average absolute deviation: you can estimate the typical estimate of these deviations. If we average the values, negative deviations will displace positive ones. Also, the sum of deviations from the mean is always zero. Thus, this is a simple approach for averaging the deviation itself. 

    Example:

     Sequence: [2, 4, 6, 8] Mean = 5 Deviation around mean = [-3, -1, 1, 3] Mean Absolute Deviation = (3 + 1 + 1 + 3) / 4 

    # Average Absolute Deviation

      

    import numpy as np

     

    def mad (data):

    return np.mean (np.absolute (

    data - np.mean (data)))

      

    Sequence = [ 2 , 4 , 6 , 8

      

    print ( "Mean Absolute Deviation: " , mad (Sequence))

    Output:

     Mean Absolute Deviation: 2.0 




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