What is the IQR method for outlier detection?

The IQR method identifies outliers using the interquartile range. Values below Q1 - 1.5×IQR or above Q3 + 1.5×IQR are considered mild outliers. This 1.5 multiplier was chosen by John Tukey to balance sensitivity and specificity.

Why use 1.5 times IQR for outlier detection?

The 1.5×IQR rule provides approximately 99.3% coverage for normal distributions while remaining robust to skewness. It's a practical balance that catches extreme values without flagging too many borderline cases.

What is the difference between mild and extreme outliers?

Mild outliers fall between 1.5×IQR and 3×IQR from the quartiles. Extreme outliers are beyond 3×IQR. Extreme outliers are much rarer and more likely to be data errors or truly exceptional cases.

Is IQR method better than standard deviation for outlier detection?

IQR is better for skewed data or non-normal distributions because it's resistant to extreme values. Standard deviation-based methods (like z-scores) assume normality and can be distorted by the outliers you're trying to detect.

Complete Guide to IQR Method Outlier Detection

Name: PlotNerd
Author: PlotNerd

1. What is the IQR Method?

The Interquartile Range (IQR) method detects outliers by measuring the middle 50% of a dataset. It uses quartiles (Q1 and Q3) to identify data points that fall significantly below or above the majority of values.

IQR-based outlier detection is widely used because it is non-parametric (no distribution assumptions) and robust to extreme values.

💡 Key Formula

IQR = Q3 − Q1

Q1 is the 25th percentile, Q3 is the 75th percentile.

2. How to Calculate IQR Step-by-Step

Step-by-Step Workflow

Sort the dataset in ascending order.
Compute Q1 (lower quartile): the median of the lower half of data.
Compute Q3 (upper quartile): the median of the upper half of data.
Calculate IQR: subtract Q1 from Q3.

📊 Example Dataset

Data: [12, 14, 16, 19, 22, 24, 27, 35]

Q1 = median of [12, 14, 16, 19] = (14 + 16) / 2 = 15

Q3 = median of [22, 24, 27, 35] = (24 + 27) / 2 = 25.5

IQR = 25.5 − 15 = 10.5

3. Tukey Fences and Outlier Classification

Tukey fences define the boundaries beyond which data points are flagged as outliers. The standard multipliers are 1.5×IQR for "mild" outliers and 3.0×IQR for "extreme" outliers.

Standard Fences

Lower Fence: Q1 − 1.5 × IQR
Upper Fence: Q3 + 1.5 × IQR
Points outside fences = potential outliers

Extended Fences

Lower Extreme Fence: Q1 − 3 × IQR
Upper Extreme Fence: Q3 + 3 × IQR
Points beyond extreme fences = strong anomalies

⚠️ Remember

The 1.5×IQR multiplier is a convention, not a universal rule. For sensitive domains like finance or healthcare, adjust the multiplier or compare with robust methods like MAD outlier detection.

4. Worked Examples

Example 1: Quality Control Data

Scenario: Manufacturing sensor readings (units: mm): [10.1, 10.3, 10.4, 10.5, 10.6, 10.7, 10.9, 12.0]

Q1 = 10.35, Q3 = 10.8 → IQR = 0.45
Lower fence = 10.35 − 1.5 × 0.45 = 9.675
Upper fence = 10.8 + 1.5 × 0.45 = 11.475
Value 12.0 exceeds the upper fence → flagged as outlier

→ Detect this in PlotNerd →

Example 2: Customer Spending

Scenario: Monthly spending for 12 customers (USD): [120, 140, 155, 160, 170, 175, 180, 190, 205, 210, 225, 500]

Q1 = 157.5, Q3 = 205 → IQR = 47.5
Upper fence = 205 + 1.5 × 47.5 = 276.25
Value 500 is an outlier → investigate spending anomaly

→ Try customer data in PlotNerd →

5. Advantages & Limitations

✅ Advantages

Robust to extreme values
No distribution assumptions
Simple to explain and implement
Powers standard box plot visualizations
Works well with skewed distributions

⚠️ Limitations

Assumes consistent scale across data
Threshold (1.5×IQR) may need tuning
Can miss clusters of legitimate extreme values
Not ideal for very small sample sizes

6. IQR vs Other Outlier Detection Methods

Method	Best For	Strengths	Considerations
IQR (1.5×)	General-purpose, skewed data	Robust to outliers, easy to explain	Threshold may need adjustment
MAD	Highly skewed or heavy-tailed data	Uses median-based scale, very robust	Less intuitive, requires modified Z-score
Z-Score	Normally distributed data	Simple computation	Sensitive to outliers and skewness
Percentile Rules	Custom thresholds (e.g., 1st/99th)	Flexible	Requires domain knowledge

Combine IQR with MAD detection or enable notched box plots in PlotNerd to highlight statistical significance.

7. Implementation Checklist

Ensure data is numeric and free from invalid entries
Decide whether to include/exclude outliers after detection
Document the multiplier (1.5× or custom) used in reports
Report central tendency alongside spread (see mean vs median vs mode).
Compare IQR results with MAD for heavy-tailed data
Visualize results in PlotNerd to communicate findings

8. FAQ

Q: Can I change the 1.5× multiplier?

A: Yes. Adjust the multiplier based on your tolerance for outliers. For highly regulated industries, consider 1.0×. For exploratory analysis, 2.0× can reduce false positives.

Q: Does IQR work on small datasets?

A: IQR is less reliable when sample size < 8. In such cases, supplement with domain knowledge or collect more data.

Q: How does IQR handle skewed data?

A: IQR performs well with skewed data because it focuses on quartiles. For heavily skewed distributions, compare results with MAD detection.

Q: Can I automate IQR detection?

A: Yes. Use PlotNerd's calculator or implement IQR logic in code (R, Python, Excel). Always log the multiplier and decisions for audit trails.

9. Conclusion

The IQR method is a reliable starting point for outlier detection. It balances simplicity with robustness, making it ideal for exploratory data analysis, reporting, and automated quality checks.

Combine IQR with visual tools like box plots and additional metrics (MAD, z-scores) to validate findings and communicate insights effectively.

Ready to Detect Outliers?

Use PlotNerd's IQR Outlier Detector to compute quartiles, IQR, and Tukey fences instantly. Supports both Tukey and MAD methods for robust outlier detection.

Open IQR Outlier Detector

📖 Related Articles

🛠️ Related Tools

→ IQR Outlier Detector Tool – Detect outliers using Tukey and MAD methods
→ Quartile Calculator – Calculate quartiles and create box plots