Write a Python program to find the mean absolute deviation of rows and columns in a dataframe

Mean Absolute Deviation (MAD) measures the average distance between each data point and the mean of the dataset. In pandas, you can calculate MAD for both rows and columns of a DataFrame using the mad() method.

What is Mean Absolute Deviation?

MAD is calculated as the mean of absolute deviations from the arithmetic mean:

MAD = mean(|x - mean(x)|)

Creating a Sample DataFrame

Let's start by creating a DataFrame with sample data ?

import pandas as pd

data = {"Column1": [6, 5.3, 5.9, 7.8, 7.6, 7.45, 7.75],
        "Column2": [7, 7.1, 7.2, 6, 6.1, 6.3, 5.1]}
df = pd.DataFrame(data)
print("DataFrame is:")
print(df)

DataFrame is:
   Column1  Column2
0     6.00      7.0
1     5.30      7.1
2     5.90      7.2
3     7.80      6.0
4     7.60      6.1
5     7.45      6.3
6     7.75      5.1

Mean Absolute Deviation of Columns

To calculate MAD for each column (default behavior), use df.mad() or df.mad(axis=0) ?

import pandas as pd

data = {"Column1": [6, 5.3, 5.9, 7.8, 7.6, 7.45, 7.75],
        "Column2": [7, 7.1, 7.2, 6, 6.1, 6.3, 5.1]}
df = pd.DataFrame(data)

print("MAD of columns:")
print(df.mad())

MAD of columns:
Column1    0.938776
Column2    0.600000
dtype: float64

Mean Absolute Deviation of Rows

To calculate MAD for each row, use df.mad(axis=1) ?

import pandas as pd

data = {"Column1": [6, 5.3, 5.9, 7.8, 7.6, 7.45, 7.75],
        "Column2": [7, 7.1, 7.2, 6, 6.1, 6.3, 5.1]}
df = pd.DataFrame(data)

print("MAD of rows:")
print(df.mad(axis=1))

MAD of rows:
0    0.500
1    0.900
2    0.650
3    0.900
4    0.750
5    0.575
6    1.325
dtype: float64

Complete Example

Here's the complete program to calculate both column and row MAD ?

import pandas as pd

data = {"Column1": [6, 5.3, 5.9, 7.8, 7.6, 7.45, 7.75],
        "Column2": [7, 7.1, 7.2, 6, 6.1, 6.3, 5.1]}
df = pd.DataFrame(data)

print("DataFrame is:")
print(df)
print("\nMAD of columns:")
print(df.mad())
print("\nMAD of rows:")
print(df.mad(axis=1))

DataFrame is:
   Column1  Column2
0     6.00      7.0
1     5.30      7.1
2     5.90      7.2
3     7.80      6.0
4     7.60      6.1
5     7.45      6.3
6     7.75      5.1

MAD of columns:
Column1    0.938776
Column2    0.600000
dtype: float64

MAD of rows:
0    0.500
1    0.900
2    0.650
3    0.900
4    0.750
5    0.575
6    1.325
dtype: float64

Key Points

• df.mad() or df.mad(axis=0) calculates MAD for columns
• df.mad(axis=1) calculates MAD for rows
• MAD measures the average distance from the mean, useful for understanding data spread
• Higher MAD values indicate greater variability in the data

Conclusion

Use df.mad() to calculate mean absolute deviation for columns and df.mad(axis=1) for rows. MAD is a robust measure of variability that's less sensitive to outliers than standard deviation.