Mean Absolute Error (MAE)

Start With The Problem

You trained a house price prediction model. Now you want to know — how good is my model?

Your model made these predictions:

House	Actual Price	Predicted Price
1	₹50 L	₹45 L
2	₹80 L	₹85 L
3	₹60 L	₹58 L
4	₹90 L	₹95 L
5	₹70 L	₹65 L

You need one single number that tells you — on average, by how much is my model wrong?

That number is MAE.

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What is MAE?

MAE = Average of absolute differences between actual and predicted values

Three steps only:

1. Find the error (Actual − Predicted) for each row
2. Make all errors positive (take absolute value)
3. Take the average

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The Formula

MAE = (1/n) × Σ |Actual - Predicted|

• n = total number of predictions
• | | = absolute value (just remove the minus sign)
• Σ = sum of everything

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Manual Walkthrough — Step by Step

House	Actual	Predicted	Error (A-P)	|Error|
1	50	45	+5	5
2	80	85	-5	5
3	60	58	+2	2
4	90	95	-5	5
5	70	65	+5	5

Step 1 — Sum of absolute errors:

5 + 5 + 2 + 5 + 5 = 22

Step 2 — Divide by n (5 houses):

MAE = 22 / 5 = 4.4

Result: MAE = 4.4 Lakhs

This means — on average, your model is wrong by ₹4.4 Lakhs per house. Simple and clear.

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Why Absolute Value? Why Not Just Average the Errors?

Without absolute value:

Errors = +5, -5, +2, -5, +5
Sum    = +5 - 5 + 2 - 5 + 5 = 2
Avg    = 2 / 5 = 0.4

This says model is almost perfect — but it's clearly not! Positive and negative errors cancel each other out and give a false picture.

Absolute value fixes this — every error counts as positive, no cancellation.

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Python Program

    import numpy as np
    import pandas as pd
    from sklearn.metrics import mean_absolute_error
    import matplotlib.pyplot as plt
    # --- Data ---
    actual    = [50, 80, 60, 90, 70]
    predicted = [45, 85, 58, 95, 65]
    # --- Manual Calculation ---
    errors          = [a - p for a, p in zip(actual, predicted)]
    absolute_errors = [abs(e) for e in errors]
    mae_manual      = sum(absolute_errors) / len(absolute_errors)
    print("=== Manual Calculation ===")
    print(f"Errors          : {errors}")
    print(f"Absolute Errors : {absolute_errors}")
    print(f"MAE (manual)    : {mae_manual}")
    # --- Using NumPy ---
    mae_numpy = np.mean(np.abs(np.array(actual) - np.array(predicted)))
    print(f"\nMAE (numpy)     : {mae_numpy}")
    # --- Using Scikit-learn ---
    mae_sklearn = mean_absolute_error(actual, predicted)
    print(f"MAE (sklearn)   : {mae_sklearn}")
    # --- DataFrame view ---
    df = pd.DataFrame({
        'Actual'         : actual,
        'Predicted'      : predicted,
        'Error'          : errors,
        'Absolute Error' : absolute_errors
    })
    print(f"\n{df.to_string(index=False)}")
    # --- Plot ---
    x = range(1, len(actual) + 1)
    plt.figure(figsize=(10, 5))
    plt.plot(x, actual,    label='Actual',    marker='o', linewidth=2)
    plt.plot(x, predicted, label='Predicted', marker='s', linewidth=2, linestyle='--')
    for i in x:
        plt.vlines(i, min(actual[i-1], predicted[i-1]),
                    max(actual[i-1], predicted[i-1]),
                    colors='red', linewidth=2, alpha=0.6)
    plt.title(f'Actual vs Predicted (MAE = {mae_sklearn})')
    plt.xlabel('House')
    plt.ylabel('Price (Lakhs)')
    plt.legend()
    plt.grid(True)
    plt.tight_layout()
    plt.savefig('mae_plot.png')
    plt.show()
    print("\nPlot saved!")

Output:

=== Manual Calculation ===

Errors          : [5, -5, 2, -5, 5]

Absolute Errors : [5, 5, 2, 5, 5]

MAE (manual)    : 4.4

MAE (numpy)     : 4.4

MAE (sklearn)   : 4.4

 Actual  Predicted  Error  Absolute Error

     50         45      5               5

     80         85     -5               5

     60         58      2               2

     90         95     -5               5

     70         65      5               5

Plot saved!

The red vertical lines in the plot show the error for each prediction — MAE is just the average length of those red lines.

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How to Read MAE

MAE is in the same unit as your target variable.

Target	MAE = 4.4 means
House Price (Lakhs)	Wrong by ₹4.4L on average
Temperature (°C)	Wrong by 4.4°C on average
Sales (units)	Wrong by 4.4 units on average

This is MAE's biggest strength — it's directly interpretable. No unit conversion needed.

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MAE vs Other Metrics — When to Use What

Metric	Penalizes Big Errors?	Interpretable?	Use When
MAE	No (equal weight)	✅ Yes, same unit	Outliers exist, you want simple average error
MSE	Yes (squares errors)	❌ Squared unit	Big errors are very bad, want to penalize them hard
RMSE	Yes	✅ Yes, same unit	Big errors are bad but want interpretable result

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The One Weakness of MAE

MAE treats all errors equally. A ₹2L error and a ₹20L error both just get added as-is.

Error of 2  → contributes 2
Error of 20 → contributes 20

If you want your model to heavily penalize large mistakes, use MSE or RMSE instead. But if outliers exist in your data and you don't want them to dominate the metric — MAE is safer.

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Real ML Project Usage

    from sklearn.metrics import mean_absolute_error
    from sklearn.linear_model import LinearRegression
    from sklearn.model_selection import train_test_split
    # After training your model
    X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)
    model = LinearRegression()
    model.fit(X_train, y_train)
    y_pred = model.predict(X_test)
    # Evaluate
    mae = mean_absolute_error(y_test, y_pred)
    print(f"Model MAE: {mae:.2f}")
    # Rule of thumb — MAE should be small relative to your target's range
    print(f"Target range : {y_test.max() - y_test.min():.2f}")
    print(f"MAE as % of range: {(mae / (y_test.max() - y_test.min())) * 100:.1f}%")

MAE as % of range is a great sanity check — if MAE is 5% of the range, your model is decent. If it's 40%, your model needs work.

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One Line Summary

MAE tells you — on average, by how much is your model's prediction off from the real value — in the same unit as your data, making it the most human-readable regression metric.