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Calculating the interquartile range (IQR) is a fundamental step in understanding the variability of real-world data. The IQR measures the spread of the middle 50% of values in a dataset, making it a robust statistic for exploratory data analysis. The IQR is defined mathematically as:

\text{IQR} = Q_3 - Q_1

where $Q_1$ is the first quartile (25th percentile) and $Q_3$ is the third quartile (75th percentile). By computing the IQR for each feature in your dataset, you can quickly identify which variables have higher variability and which are more tightly clustered. This insight is crucial for detecting outliers, comparing distributions, and making informed decisions about data preprocessing.


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import pandas as pd

# Load a sample dataset
data = {
    'age': [23, 45, 31, 35, 40, 29, 48, 34, 37, 42],
    'income': [50000, 80000, 62000, 76000, 54000, 70000, 90000, 65000, 71000, 85000],
    'score': [88, 92, 85, 90, 87, 91, 95, 89, 86, 93]
}
df = pd.DataFrame(data)

# Compute Q1 and Q3 for each column
q1 = df.quantile(0.25)
q3 = df.quantile(0.75)

# Compute the IQR for each column
iqr = q3 - q1

# Summarize results in a DataFrame
iqr_summary = pd.DataFrame({
    'Q1': q1,
    'Q3': q3,
    'IQR': iqr
})

print(iqr_summary)

The output DataFrame displays the first quartile ( $Q_1$ ), third quartile ( $Q_3$ ), and IQR for each feature. Higher IQR values indicate greater variability in the middle 50% of the data for that column, while lower IQR values suggest that most values are clustered closely together. For instance, if the $\text{income}$ column shows a much larger IQR than $\text{score}$ , it means that incomes vary more widely among the subjects than their scores do. By comparing IQRs across features, you gain a clearer picture of which variables are more dispersed and which are more consistent, helping you focus your analysis on the most variable or stable aspects of your data.

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