How to Detect Outliers in Python Using the Interquartile Range (IQR)

When cleaning tabular data or preprocessing datasets for machine learning models, identifying outliers is a critical step. Outliers can skew statistical distributions and negatively impact model training performance.

The Interquartile Range (IQR) method is a simple, non-parametric approach to detecting extreme values without assuming a normal distribution.

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What is the Interquartile Range (IQR)?

The IQR measures the spread of the middle 50% of your data. It is calculated as the difference between the 75th percentile ($Q_3$) and the 25th percentile ($Q_1$):
IQR Outlier Calculator

$$\text{IQR} = Q_3 - Q_1$$

Outlier Thresholds

Using the 1.5 $\times$ IQR rule, data points are flagged as outliers if they fall outside these boundary limits:

• Lower Bound: $Q_1 - (1.5 \times \text{IQR})$
• Upper Bound: $Q_3 + (1.5 \times \text{IQR})$

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Python Implementation

You can implement IQR outlier detection in Python using pandas and numpy:

python
import pandas as pd
import numpy as np

def detect_outliers_iqr(data: pd.Series):
    """
    Returns lower bound, upper bound, and flagged outliers in a Series.
    """
    q1 = data.quantile(0.25)
    q3 = data.quantile(0.75)
    iqr = q3 - q1

    lower_bound = q1 - (1.5 * iqr)
    upper_bound = q3 + (1.5 * iqr)

    outliers = data[(data < lower_bound) | (data > upper_bound)]
    return lower_bound, upper_bound, outliers

# Example dataset
scores = pd.Series([12, 14, 15, 18, 19, 19, 21, 23, 24, 105])
lower, upper, outliers = detect_outliers_iqr(scores)

print(f"Lower Bound: {lower}")
print(f"Upper Bound: {upper}")
print(f"Detected Outliers:\n{outliers.tolist()}")