To **center** a dataset means to subtract the mean value from each individual observation in the dataset.

Once you’ve centered a dataset, the mean value of the dataset becomes zero.

The following examples show how to center data in Python.

**Example 1: Center the Values of a NumPy Array**

Suppose we have the following NumPy array:

import numpy as np #create NumPy array data = np.array([4, 6, 9, 13, 14, 17, 18, 19, 19, 21]) #display mean of array print(data.mean()) 14.0

We can define a function to subtract the mean value of the array from each individual observation:

#create function to center data center_function = lambda x: x - x.mean() #apply function to original NumPy array data_centered = center_function(data) #view updated Array print(data_centered) array([-10., -8., -5., -1., 0., 3., 4., 5., 5., 7.])

The resulting values are the centered values of the dataset.

Since the mean of the original array was 14, this function simply subtracted 14 from each individual value in the original array.

For example:

- 1st value in centered array = 4 – 14 =
**-10** - 2nd value in centered array = 6 – 14 =
**-8** - 3rd value in centered array = 9 – 14 =
**-5**

And so on.

We can also verify that the mean of the centered array is zero:

#display mean of centered array print(data_centered.mean()) 0.0

**Example 2: Center the Columns of a Pandas DataFrame**

Suppose we have the following pandas DataFrame:

import pandas as pd #create DataFrame df = pd.DataFrame({'x': [1, 4, 5, 6, 6, 8, 9], 'y': [7, 7, 8, 8, 8, 9, 12], 'z': [3, 3, 4, 4, 6, 7, 7]}) #view DataFrame print(df) x y z 0 1 7 3 1 4 7 3 2 5 8 4 3 6 8 4 4 6 8 6 5 8 9 7 6 9 12 7

We can use the pandas **apply()** function to center the values of each column in the DataFrame:

#center the values in each column of the DataFrame df_centered = df.apply(lambda x: x-x.mean()) #view centered DataFrame print(df_centered) x y z 0 -4.571429 -1.428571 -1.857143 1 -1.571429 -1.428571 -1.857143 2 -0.571429 -0.428571 -0.857143 3 0.428571 -0.428571 -0.857143 4 0.428571 -0.428571 1.142857 5 2.428571 0.571429 2.142857 6 3.428571 3.571429 2.142857

We can then verify that the mean value of each column is zero:

#display mean of each column in the DataFrame df_centered.mean() x 2.537653e-16 y -2.537653e-16 z 3.806479e-16 dtype: float64

The column means are shown in scientific notation, but each value is essentially equal to zero.

**Additional Resources**

The following tutorials explain how to perform other common operations in Python:

How to Calculate a Trimmed Mean in Python

How to Calculate Mean Squared Error (MSE) in Python

How to Calculate the Average of Selected Columns in Pandas