Outlier Detection (IQR Method)

What is IQR?

The Interquartile Range (IQR) is:

Q3 (75th percentile) − Q1 (25th percentile)

A common rule flags outliers outside:

Lower bound = Q1 − 1.5 × IQR
Upper bound = Q3 + 1.5 × IQR

Example

IQR bounds

import pandas as pd
 
df = pd.DataFrame({"amount": [100, 110, 120, 115, 105, 130, 125, 3000]})
 
q1 = df["amount"].quantile(0.25)
q3 = df["amount"].quantile(0.75)
iqr = q3 - q1
 
lower = q1 - 1.5 * iqr
upper = q3 + 1.5 * iqr
 
print("Q1:", q1)
print("Q3:", q3)
print("IQR:", iqr)
print("Bounds:", lower, upper)
 
outliers = df[(df["amount"] < lower) | (df["amount"] > upper)]
print(outliers)

IQR bounds

import pandas as pd
 
df = pd.DataFrame({"amount": [100, 110, 120, 115, 105, 130, 125, 3000]})
 
q1 = df["amount"].quantile(0.25)
q3 = df["amount"].quantile(0.75)
iqr = q3 - q1
 
lower = q1 - 1.5 * iqr
upper = q3 + 1.5 * iqr
 
print("Q1:", q1)
print("Q3:", q3)
print("IQR:", iqr)
print("Bounds:", lower, upper)
 
outliers = df[(df["amount"] < lower) | (df["amount"] > upper)]
print(outliers)

Flag outliers (keep rows, add a column)

Outlier flag

df["is_outlier"] = (df["amount"] < lower) | (df["amount"] > upper)
print(df)

Outlier flag

df["is_outlier"] = (df["amount"] < lower) | (df["amount"] > upper)
print(df)

Notes

IQR is robust for skewed data.
Outlier detection is not outlier removal.
Always validate outliers with domain context.

Visualize it

diagram IQR outlier detection mermaid

  flowchart LR
  A["Sort the values"] --> B["Compute Q1 and Q3"]
  B --> C["IQR = Q3 - Q1"]
  C --> D["Lower fence = Q1 - 1.5*IQR
Upper fence = Q3 + 1.5*IQR"]
  D --> E["Flag values outside the fences"]

Values are sorted, quartiles are computed, and anything outside the fences is flagged as an outlier.

A box plot is just this rule drawn as a picture: the box spans Q1 to Q3, the whiskers reach out to the fences, and anything past them is plotted as its own dot.

sketch Boxplot with IQR fences p5.js

The box covers Q1-Q3, whiskers extend to the fences, and points beyond the fences are outliers.

🧪 Try It Yourself

Exercise 1 – Compute Q1, Q3, and IQR

Exercise 2 – Compute the fences

Exercise 3 – Flag the outliers

Detection is only half the job — see Handling Outliers for what to actually do once you’ve found them.

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