IQR Calculator (Interquartile Range)
Free IQR calculator. Compute Q1, Q2, Q3, IQR, Semi-IQR. Inner and outer fences. Mild and extreme out
Why This Statistical Analysis Matters
Why: Statistical calculator for analysis.
How: Enter inputs and compute results.
IQR Calculator — Quartiles, Fences, Outlier Detection
Compute Q1, Q2, Q3, IQR, Semi-IQR. Identify mild and extreme outliers with 1.5×IQR and 3×IQR rules. Box plot with fences.
Real-World Scenarios — Click to Load
Data Input
Box Plot with Fences
Rose dashed = inner fences (1.5×IQR); Red dotted = outer fences (3×IQR). Rose points = mild outliers; Red = extreme.
Quartiles & Fences Comparison
Data with Outliers Highlighted
Blue = normal; Rose = mild outlier; Red = extreme outlier.
Calculation Breakdown
For educational and informational purposes only. Verify with a qualified professional.
Key Takeaways
- • IQR = Q3 − Q1 measures the spread of the middle 50% of the data
- • Lower inner fence = Q1 − 1.5×IQR; Upper inner fence = Q3 + 1.5×IQR — mild outliers outside these
- • Lower outer fence = Q1 − 3×IQR; Upper outer fence = Q3 + 3×IQR — extreme outliers beyond these
- • Semi-IQR (Quartile Deviation) = IQR/2 — a robust measure of spread
- • Mild outliers: between inner and outer fences; Extreme outliers: beyond outer fences
- • IQR is robust to outliers — unlike range or standard deviation
Did You Know?
How It Works
1. Sort the Data
Arrange all values in ascending order. Quartiles are computed from the sorted data.
2. Compute Q1, Q2, Q3
Q1 = 25th percentile, Q2 = median (50th), Q3 = 75th percentile. Choose inclusive, exclusive, or interpolation method.
3. Calculate IQR and Semi-IQR
IQR = Q3 − Q1. Semi-IQR (Quartile Deviation) = IQR/2.
4. Inner and Outer Fences
Inner: Q1 ± 1.5×IQR. Outer: Q1 ± 3×IQR. Values between inner and outer = mild outliers; beyond outer = extreme.
5. Classify Outliers
Mild outliers fall between inner and outer fences. Extreme outliers fall beyond the outer fences.
Expert Tips
Quartile Method
Inclusive matches Excel; Exclusive matches R type 7; Interpolation uses linear (n+1) method.
Outlier Handling
Don't remove outliers blindly. Investigate whether they are data errors or genuine extremes.
Semi-IQR
Quartile Deviation = IQR/2. Used in coefficient of quartile variation and some robust statistics.
1.5× vs 3× Rule
1.5×IQR flags mild outliers; 3×IQR flags extreme. Adjust for very skewed or small samples if needed.
Why Use This Calculator vs Other Tools?
| Feature | This Calculator | Excel | R | Python |
|---|---|---|---|---|
| Q1, Q2, Q3, IQR | ✅ | ⚠️ Multiple functions | ✅ | ✅ |
| Inner + outer fences | ✅ | ❌ | ⚠️ Manual | ⚠️ Manual |
| Mild vs extreme outliers | ✅ | ❌ | ⚠️ | ⚠️ |
| Semi-IQR (Quartile Dev) | ✅ | ❌ | ⚠️ | ⚠️ |
| Box plot with fences | ✅ | ❌ | ✅ | ✅ |
| Educational content | ✅ | ❌ | ❌ | ❌ |
| Copy & share results | ✅ | ❌ | ❌ | ❌ |
| AI-powered interpretation | ✅ | ❌ | ❌ | ❌ |
Frequently Asked Questions
What is the 1.5×IQR rule?
Tukey's rule: values outside [Q1−1.5×IQR, Q3+1.5×IQR] are mild outliers. Values outside 3×IQR are extreme outliers.
What is Semi-IQR?
Semi-IQR (Quartile Deviation) = IQR/2. It measures half the spread of the middle 50% of data.
Inclusive vs exclusive vs interpolation?
Different formulas for percentile rank. Inclusive matches Excel; Exclusive matches R; Interpolation uses (n+1) linear method.
When to use IQR vs standard deviation?
Use IQR for skewed data or when you want robustness to outliers. SD is better for symmetric, roughly normal data.
What are mild vs extreme outliers?
Mild: between inner (1.5×IQR) and outer (3×IQR) fences. Extreme: beyond outer fences.
How do I read the box plot with fences?
Rose dashed lines = inner fences; Red dotted lines = outer fences. Rose points = mild outliers; Red = extreme.
What is the Quartile Deviation Coefficient?
IQR/(Q3+Q1). A dimensionless relative spread measure, useful for comparing across different scales.
How many data points do I need?
At least 2. For meaningful IQR and outlier detection, n ≥ 5 is recommended.
IQR by the Numbers
Formulas Reference
IQR = Q3 − Q1
Semi-IQR (Quartile Deviation) = IQR / 2
Lower inner fence = Q1 − 1.5×IQR
Upper inner fence = Q3 + 1.5×IQR
Lower outer fence = Q1 − 3×IQR
Upper outer fence = Q3 + 3×IQR
Official Data Sources
Disclaimer: Quartile methods can yield different Q1/Q3 values. For publication, state which method you used.
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