Understanding Types of Means | Set 1

It is one of the most important concepts of statistics, a crucial subject to learn Machine Learning.

• Arithmetic Mean : It is the mathematical expectation of a discrete set of numbers or average.
Denoted by , pronounced as “x-bar”. It is the sum of all the discrete values in the set divided by the total number of values in the set.
The formula to calculate the mean of n values – x1, x2, ….. xn Example –

Sequence = {1, 5, 6, 4, 4}

Sum             = 20
n, Total values = 5
Arithmetic Mean = 20/5 = 4

Code –

 # Arithmetic Mean    import statistics     # discrete set of numbers data1 = [1, 5, 6, 4, 4]     x = statistics.mean(data1)     # Mean  print("Mean is :", x)

Output :

Mean is : 4

• Trimmed Mean : Arithmetic Mean is influenced by the outliers (extreme values) in the data. So, trimmed mean in used at the time of pre-processing when we are handling such kinds of data in machine learning.
It is arithmetic having a variation i.e. it is calculated by dropping a fixed number of sorted values from each end of the sequence of data given and then calculated the mean (average) of remaining values. Example –

Sequence = {0, 2, 1, 3}
p        = 0.25

Remaining Sequemce  = {2, 1}
n, Total values = 2
Mean = 3/2 = 1.5

Code –

 # Trimmed Mean     from scipy import stats    # discrete set of numbers data = [0, 2, 1, 3]     x = stats.trim_mean(data, 0.25)    # Mean  print("Trimmed Mean is :", x)

Output :

Trimmed Mean is : 1.5
• Weighted Mean : Arithmetic Mean or Trimmed mean is giving equal importance to all the parameters involved. But whenever we are working in machine learning predictions, there is a possibility that some parameter values hold more importance than the others, so we assign high weights to the values of such parameters. Also, there can be a chance that our data set has a highly variable value of a parameter, so we assign lesser weights to the values of such parameters. Example –

Sequence = [0, 2, 1, 3]
Weight   = [1, 0, 1, 1]

Sum (Weight * sequence)  = 0*1 + 2*0 + 1*1 + 3*1
Sum (Weight) = 3
Weighted Mean = 4 / 3 = 1.3333333333333333

Code 1 –

 # Weighted Mean     import numpy as np    # discrete set of numbers data = [0, 2, 1, 3]     x = np.average(data, weights =[1, 0, 1, 1])    # Mean  print("Weighted Mean is :", x)

Output 1 :

Weighted Mean is : 1.3333333333333333

Code 2 –

 # Weighted Mean     data = [0, 2, 1, 3] weights = [1, 0, 1, 1]    x = sum(data[i] * weights[i]      for i in range(len(data))) / sum(weights)       print ("Weighted Mean is :", x)

Output 2 :

Weighted Mean is : 1.3333333333333333

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