Box Plot — Five Number Summary & Outliers
Min, Q1, median, Q3, max. IQR = Q3−Q1. Tukey fences at 1.5×IQR. Compare groups, spot skewness and outliers.
Why This Statistical Analysis Matters
Why: Box plots summarize distribution without assuming normality. Compare groups side-by-side. Tukey (1977) standard for exploratory data analysis.
How: Enter data (comma separated). One or more groups. Get five-number summary, IQR, fences, outlier list, and box-and-whisker visualization.
- ●IQR = Q3 − Q1
- ●1.5×IQR fence rule
- ●Tukey 1977
Box-and-Whisker Plots — Quartiles, IQR, Fences, Outlier Detection
Visualize distribution shape, center, spread, and outliers. Compare groups side-by-side with quartiles, IQR, and the 1.5×IQR rule.
Real-World Scenarios — Click to Load
Data Input
Group 1 (n=13)
Box-and-Whisker Plot
Data Strip Plot
Five-Number Summary
Calculation Breakdown
For educational and informational purposes only. Verify with a qualified professional.
📈 Statistical Insights
25th and 75th percentile
— Quartiles
Q3 − Q1, middle 50%
— Spread
Tukey fence multiplier
— Outliers
Key Takeaways
- • Box plot shows five-number summary: Min, Q1, Median (Q2), Q3, Max
- • IQR = Q3 − Q1 measures spread of the middle 50%
- • Tukey fences: Lower = Q1 − 1.5×IQR, Upper = Q3 + 1.5×IQR
- • Mild outliers: outside 1.5×IQR; Extreme: outside 3×IQR
- • Whiskers extend to min/max data points within fences
Did You Know?
Expert Tips
Quartile Method
Inclusive (default) matches many software; Exclusive matches R type 7.
Outlier Investigation
Don't remove outliers blindly — investigate whether they are errors or genuine.
Sample Size
Box plots work best with n ≥ 5; for very small n, consider a strip plot.
1.5×IQR Rule
Tukey's rule of thumb; adjust for very skewed or small samples if needed.
When to Use Box Plots
| Scenario | Use Box Plot? |
|---|---|
| Comparing multiple groups | ✅ Ideal |
| Spotting outliers quickly | ✅ Ideal |
| Showing five-number summary | ✅ Ideal |
| Detailed distribution shape | ⚠️ Histogram better |
| Very small n (< 5) | ⚠️ Strip plot better |
Why Use This Calculator vs Other Tools?
| Feature | This Calculator | Excel | R boxplot |
|---|---|---|---|
| Box + strip plot | ✅ | ⚠️ Manual | ✅ |
| Multiple groups | ✅ | ⚠️ Manual | ✅ |
| Quartile method choice | ✅ | ❌ | ✅ |
| Outlier list + fences | ✅ | ❌ | ⚠️ |
| Step-by-step breakdown | ✅ | ❌ | ❌ |
| 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. Outside 3×IQR are extreme outliers.
How do I read skewness from a box plot?
If the median is closer to Q1, the distribution is right-skewed. If closer to Q3, left-skewed. Symmetric box suggests symmetry.
What is the difference between inclusive and exclusive quartiles?
Inclusive uses interpolation including endpoints; Exclusive uses a different formula. Results can differ slightly for small samples.
When should I use a box plot vs histogram?
Box plots are better for comparing groups and spotting outliers. Histograms show shape in more detail for a single distribution.
Do whiskers always extend to min and max?
No. Whiskers extend to the furthest data point within the fences. Outliers are plotted separately.
How do I compare two datasets with box plots?
Place them side-by-side. Compare medians (center), IQR (spread), whisker lengths (skew), and number of outliers.
Box Plot by the Numbers
Official Data Sources
Disclaimer: Quartile methods (inclusive vs exclusive) can yield different Q1/Q3 values. This calculator uses linear interpolation. For publication, state which method you used.
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