*16*

To **standardize** a dataset means to scale all of the values in the dataset such that the mean value is 0 and the standard deviation is 1.

We use the following formula to standardize the values in a dataset:

**x _{new} = (x_{i} – x) / s**

where:

**x**: The i_{i}^{th}value in the dataset**x**: The sample mean**s**: The sample standard deviation

We can use the following syntax to quickly standardize all of the columns of a pandas DataFrame in Python:

(df-df.mean())/df.std()

The following examples show how to use this syntax in practice.

**Example 1: Standardize All Columns of DataFrame**

The following code shows how to standardize all columns in a pandas DataFrame:

import pandas as pd #create data frame df = pd.DataFrame({'y': [8, 12, 15, 14, 19, 23, 25, 29], 'x1': [5, 7, 7, 9, 12, 9, 9, 4], 'x2': [11, 8, 10, 6, 6, 5, 9, 12], 'x3': [2, 2, 3, 2, 5, 5, 7, 9]}) #view data frame df y x1 x2 x3 0 8 5 11 2 1 12 7 8 2 2 15 7 10 3 3 14 9 6 2 4 19 12 6 5 5 23 9 5 5 6 25 9 9 7 7 29 4 12 9 #standardize the values in each column df_new = (df-df.mean())/df.std() #view new data frame df_new y x1 x2 x3 0 -1.418032 -1.078639 1.025393 -0.908151 1 -0.857822 -0.294174 -0.146485 -0.908151 2 -0.437664 -0.294174 0.634767 -0.525772 3 -0.577717 0.490290 -0.927736 -0.908151 4 0.122546 1.666987 -0.927736 0.238987 5 0.682756 0.490290 -1.318362 0.238987 6 0.962861 0.490290 0.244141 1.003746 7 1.523071 -1.470871 1.416019 1.768505

We can verify that the mean and standard deviation of each column is equal to 0 and 1, respectively:

#view mean of each column df_new.mean() y 0.000000e+00 x1 2.775558e-17 x2 -4.163336e-17 x3 5.551115e-17 dtype: float64 #view standard deviation of each column df_new.std() y 1.0 x1 1.0 x2 1.0 x3 1.0 dtype: float64

**Example 2: Standardize Specific Columns of DataFrame**

Sometimes you may only want to standardize specific columns in a DataFrame.

For example, for many machine learning algorithms you may only want to standardize the predictor variables before fitting a certain model to the data.

The following code shows how to standardize specific columns in a pandas DataFrame:

import pandas as pd #create data frame df = pd.DataFrame({'y': [8, 12, 15, 14, 19, 23, 25, 29], 'x1': [5, 7, 7, 9, 12, 9, 9, 4], 'x2': [11, 8, 10, 6, 6, 5, 9, 12], 'x3': [2, 2, 3, 2, 5, 5, 7, 9]}) #view data frame df y x1 x2 x3 0 8 5 11 2 1 12 7 8 2 2 15 7 10 3 3 14 9 6 2 4 19 12 6 5 5 23 9 5 5 6 25 9 9 7 7 29 4 12 9 #define predictor variable columns df_x = df[['x1', 'x2', 'x3']] #standardize the values for each predictor variable df[['x1', 'x2', 'x3']] = (df_x-df_x.mean())/df_x.std() #view new data frame df y x1 x2 x3 0 8 -1.078639 1.025393 -0.908151 1 12 -0.294174 -0.146485 -0.908151 2 15 -0.294174 0.634767 -0.525772 3 14 0.490290 -0.927736 -0.908151 4 19 1.666987 -0.927736 0.238987 5 23 0.490290 -1.318362 0.238987 6 25 0.490290 0.244141 1.003746 7 29 -1.470871 1.416019 1.768505

Notice that the “y” column remains unchanged, but the columns “x1”, “x2”, and “x3” are all standardized.

We can verify that the mean and standard deviation of each predictor variable column is equal to 0 and 1, respectively:

#view mean of each predictor variable column df[['x1', 'x2', 'x3']].mean() x1 2.775558e-17 x2 -4.163336e-17 x3 5.551115e-17 dtype: float64 #view standard deviation of each predictor variable column df[['x1', 'x2', 'x3']].std() x1 1.0 x2 1.0 x3 1.0 dtype: float64

**Additional Resources**

How to Normalize Columns in a Pandas DataFrame

How to Remove Outliers in Python

Standardization vs. Normalization: What’s the Difference?