Calculating Mean Absolute Deviation in DataFrame Rows and Columns Using Python

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πŸ’‘ Problem Formulation: Calculating the mean absolute deviation (MAD) is a statistical measure used to quantify the variability of a set of data points. In the context of a DataFrame, users might need to compute the MAD for each row and column to understand discrepancies within their dataset. This article guides you through different methods in Python to calculate the MAD for rows and columns in a DataFrame given a dataset with numerical values.

Method 1: Using DataFrame functions with apply()

This method utilizes the apply() function on the DataFrame, which allows us to apply a custom function along an axis of the DataFrame (0 for columns and 1 for rows). The custom function will calculate the mean absolute deviation for whichever series it is applied to. This method provides a direct and flexible approach.

Here’s an example:

import pandas as pd

# Define a DataFrame
df = pd.DataFrame({
    'A': [1, 2, 3],
    'B': [4, 5, 6],
    'C': [7, 8, 9]
})

# Define the MAD function
def mad(series):
    return series.mad()

# Calculate MAD for rows and columns
mad_rows = df.apply(mad, axis=1)
mad_columns = df.apply(mad)

print("MAD for rows:\n", mad_rows)
print("MAD for columns:\n", mad_columns)

The output will be:

MAD for rows:
0    2.0
1    2.0
2    2.0
dtype: float64
MAD for columns:
A    0.888889
B    0.888889
C    0.888889
dtype: float64

This code snippet creates a DataFrame with three rows and columns A, B, and C containing numbers 1 through 9. The MAD for each row and column is calculated by applying the mad() function, which is an inherent method for pandas series that computes mean absolute deviation.

Method 2: Using the mean() and abs() with subtract()

The second method entails using built-in pandas functions mean(), abs(), and subtract() to manually compute the mean absolute deviation. This method breaks down the steps of the calculation and provides insight into the underlying process.

Here’s an example:

import pandas as pd

# Define a DataFrame
df = pd.DataFrame({
    'A': [1, 2, 3],
    'B': [4, 5, 6],
    'C': [7, 8, 9]
})

# Calculate man deviations
def mad_explicit(df, axis):
    return df.sub(df.mean(axis=axis), axis=axis).abs().mean(axis=axis)

mad_rows = mad_explicit(df, 1)
mad_columns = mad_explicit(df, 0)

print("MAD for rows:\n", mad_rows)
print("MAD for columns:\n", mad_columns)

The output will be:

MAD for rows:
0    2.0
1    2.0
2    2.0
dtype: float64
MAD for columns:
A    0.888889
B    0.888889
C    0.888889
dtype: float64

This snippet entails a DataFrame similar to the first method. It then defines a function that explicitly computes the MAD by subtracting the mean from the original DataFrame values, taking absolute values, and then calculating the mean of these absolute differences.

Method 3: Using NumPy functions

This method leverages the power of NumPy to compute the mean absolute deviation. NumPy is a highly optimized library for numerical operations. By importing this library, we can apply vectorized operations which are generally faster than applying a function over DataFrame rows or columns.

Here’s an example:

import pandas as pd
import numpy as np

# Define a DataFrame
df = pd.DataFrame({
    'A': [1, 2, 3],
    'B': [4, 5, 6],
    'C': [7, 8, 9]
})

# Calculate MAD using NumPy
mad_rows = np.mean(np.abs(df.sub(df.mean(axis=1), axis=0)), axis=1)
mad_columns = np.mean(np.abs(df.sub(df.mean(axis=0), axis=1)), axis=0)

print("MAD for rows:\n", mad_rows)
print("MAD for columns:\n", mad_columns)

The output will be:

MAD for rows:
0    2.0
1    2.0
2    2.0
dtype: float64
MAD for columns:
A    0.888889
B    0.888889
C    0.888889
dtype: float64

Here, the code uses NumPy’s mean and absolute functions coupled with pandas’ DataFrame operations for an efficient computation. We still calculate the deviations by row and by column, but this time using NumPy’s optimized functions which can lead to performance benefits, especially with larger datasets.

Method 4: Using the pandas.DataFrame.mad() Method

Pandas has a built-in method specifically for calculating the mean absolute deviation, simplifying the process. The DataFrame.mad() method is straightforward and does not require any additional functions. This is the most direct method and is recommended for its simplicity and clarity.

Here’s an example:

import pandas as pd

# Define a DataFrame
df = pd.DataFrame({
    'A': [1, 2, 3],
    'B': [4, 5, 6],
    'C': [7, 8, 9]
})

# Calculate MAD using pandas built-in function
mad_rows = df.mad(axis=1)
mad_columns = df.mad()

print("MAD for rows:\n", mad_rows)
print("MAD for columns:\n", mad_columns)

The output will be:

MAD for rows:
0    2.0
1    2.0
2    2.0
dtype: float64
MAD for columns:
A    0.888889
B    0.888889
C    0.888889
dtype: float64

The code snippet uses the DataFrame.mad() method to calculate the MAD for both rows and columns. This method is Panda’s native functionality to compute mean absolute deviation, which makes the code very clean and efficient.

Bonus One-Liner Method 5: Lambda Function with apply()

As a bonus, we include a one-liner approach utilizing lambda functions with the apply() method. This method combines the functionality of an anonymous function with the flexibility of apply(), offering a concise alternative for those who prefer one-liners.

Here’s an example:

import pandas as pd

# Define a DataFrame
df = pd.DataFrame({
    'A': [1, 2, 3],
    'B': [4, 5, 6],
    'C': [7, 8, 9]
})

# One-liner MAD for rows and columns
mad_rows = df.apply(lambda x: (x-x.mean()).abs().mean(), axis=1)
mad_columns = df.apply(lambda x: (x-x.mean()).abs().mean(), axis=0)

print("MAD for rows:\n", mad_rows)
print("MAD for columns:\n", mad_columns)

The output will be:

MAD for rows:
0    2.0
1    2.0
2    2.0
dtype: float64
MAD for columns:
A    0.888889
B    0.888889
C    0.888889
dtype: float64

This concise code example uses a lambda function to compute the MAD for each row and column directly within the apply() method call, showcasing Python and pandas’ ability to write succinct and powerful expressions.

Summary/Discussion

  • Method 1: Apply with custom function. Strengths: flexible and understandable. Weaknesses: potentially slower with large datasets due to the overhead of the apply method.
  • Method 2: Explicit calculation using pandas operations. Strengths: educational, as it details each computational step. Weaknesses: verbose and less direct than other methods.
  • Method 3: NumPy Functions. Strengths: performance gain with large datasets. Weaknesses: slightly more complex due to mixing pandas and NumPy.
  • Method 4: pandas.DataFrame.mad() Method. Strengths: simple and most direct. Weaknesses: does not offer additional insight into computation process.
  • Method 5: Lambda Function with apply(). Strengths: concise, Pythonic. Weaknesses: can be harder to read and understand for beginners.