If you are given a vector X, the mean of 0 and standard deviation of 1 for X can be achieved by the following equation:

Let's see how this can be achieved in Python.

Let's import the necessary libraries to begin with. We will follow this with the generation of the input data:

# Load Libraries
import numpy as np
from sklearn.preprocessing import scale

# Input data generation
np.random.seed(10)
x = [np.random.randint(10,25)*1.0 for i in range(10)]

We are now ready to demonstrate standardization:

x_centered = scale(x,with_mean=True,with_std=False)
x_standard = scale(x,with_mean=True,with_std=True)

print x
print x_centered
print x_standard
print "Orginal x mean = %0.2f, Centered x mean = %0.2f, Std dev of 
        standard x =%0.2f"%(np.mean(x),np.mean(x_centered),np.std(x_standard))

We will generate some random data using np.random:

x = [np.random.randint(10,25)*1.0 for i in range(10)]

We will perform standardization using the scale function from scikit-learn:

x_centered = scale(x,with_mean=True,with_std=False)
x_standard = scale(x,with_mean=True,with_std=True)

The x_centered is scaled using only the mean; you can see the with_mean parameter set to True and with_std set to False.

The x_standard is standardized using both mean and standard deviation.

Now let us look at the output.

The original data is as follows:

[19.0, 23.0, 14.0, 10.0, 11.0, 21.0, 22.0, 19.0, 23.0, 10.0]

Next, we will print x_centered, where we centered it with the mean value:

[ 1.8  5.8 -3.2 -7.2 -6.2  3.8  4.8  1.8  5.8 -7.2]

Finally we will print x_standardized, where we used both the mean and standard deviation:

[ 0.35059022  1.12967961 -0.62327151 -1.4023609  -1.20758855  0.74013492
  0.93490726  0.35059022  1.12967961 -1.4023609 ]

Orginal x mean = 17.20, Centered x mean = 0.00, Std dev of standard x =1.00

Let's break the preceding equation in two parts: just the numerator part, which is called centering, and the whole equation, which is called standardization. Using the mean values, centering plays a critical role in regression. Consider a dataset that has two attributes, weight and height. We will center the data such that the predictor, weight, has a mean of 0. This makes the interpretation of intercept easier. The intercept will be interpreted as what is the expected height when the predictor values are set to their mean.