IQR vs. Standard Deviation:
Which Finds Outliers Better?
The two most common ways to find outliers often give different results. Here is how to choose the right one for your data.
At a Glance Comparison
| Feature | IQR Method (Tukey) | Standard Deviation (Z-Score) |
|---|---|---|
| Best For | Skewed or Normal Data | Strictly Normal Data |
| Robustness | High (Resistant to outliers) | Low (Influenced by outliers) |
| Definition | 1.5 Γ IQR beyond quartiles | 2 or 3 SD from mean |
| Common Use | Box Plots, EDA | Quality Control, Physics |
The IQR Method (Recommended)
The Interquartile Range (IQR) method, also known as Tukey's Fences, uses the middle 50% of your data to define what is "normal".
Why it wins:
The IQR method is robust. This means the outliers themselves don't affect the calculation of the boundaries. Even if you have a massive outlier (like 1,000,000 in a dataset of 1-10), the median and quartiles remain stable.
This is the standard method used in Box Plots. If you are doing exploratory data analysis or working with real-world data (which is rarely perfectly normal), stick with IQR.
The Standard Deviation Method (Z-Score)
This method defines outliers as data points that are more than 2 or 3 Standard Deviations away from the Mean.
The Problem (Masking Effect):
The Mean and Standard Deviation are sensitive to outliers. A single extreme value will pull the Mean towards it and inflate the Standard Deviation. This expands the "normal" range, potentially hiding (masking) the very outlier you are trying to find!
Use this method ONLY if you are certain your data follows a Normal Distribution (Bell Curve) and you are detecting anomalies in a controlled process (like manufacturing tolerances).
The Verdict
Use IQR When:
- Your data is skewed (e.g., income, house prices).
- You have a small dataset.
- You want to create a Box Plot.
- You are unsure about the distribution.
Use Standard Deviation When:
- Your data is strictly Normal (Gaussian).
- You are doing Quality Control (Six Sigma).
- You need to perform parametric statistical tests later.
PlotNerd uses the robust IQR Method by default, but also supports MAD (even more robust).
Try the IQR Calculator